1.8: Developmental Theories
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Now we will explore theories of development.
We discussed research methods in Lesson One. We are now turning our attention to theories of development. Theories are explanations about how the world works. In development, theories suggest how or why people change or remain the same over time. Theories help inform research. Theoretical concepts and assertions need to be tested through research. Theories should be modified based on research results. They are not facts. They are subject to change.
The first theories we will explore are explanations for what motivates us. They are referred to as psychodynamic theories because they suggest that psychological needs motivate our actions. These include Freud’s psychosexual theory and Erikson’s psychosocial theory.
Sigmund Freud offered the first comprehensive theory of personality: an explanation of how the management of early biological drives and motives could result in certain personality traits. He lived from 1856 to 1939 witnessing the Victorian Era in England, World War I and the start of World War II. He lived in a time in which genetics was a popular explanation for human behavior and many behaviors were believed to be instinctive. But Freud studied an ailment called hysteria that had mystified the clinical world for a long time. Hysteria was originally thought to be disorder only women suffered; it was referred to as the ‘disease of the wandering womb’ because the Greeks thought it resulted from the womb becoming dislocated in the body. When men began to suffer from hysteria-like symptoms, it was believed that only genetically inferior men were vulnerable. Freud found that genetic explanations for this disorder marked by physical writhing and uncontrollable emotion were inadequate.
Men suffering from symptoms of hysteria came from a variety of genetic backgrounds. What they all shared was the trauma of war. Freud found that when they were able to talk about this trauma or their fears of what might happen when they reached combat, their symptoms dissipated. He invented the “talking cure.” He believed that early childhood experiences were often the source of mental anguish and emphasized the importance of parenting for shaping personality. He viewed mental illness, not as a result of being evil, immoral, or diseased, but because of an inability to handle painful realities of one’s life.
Freud described a variety of defense mechanisms, or ways to distort and therefore be able to handle, painful truths. This is a partial listing and represents some of the common ways people distort reality. Few of us can handle painful experiences psychologically as soon as they happen. So don’t be worried if you can identify with some of these. That doesn’t mean you have a mental disorder! It just means that these are commonly used. To repress is to avoid thinking about something that is upsetting. It’s often recommended by others. A friend might say, “Don’t worry about it. Just stay busy.” Regression involves returning to a time in life when you felt safe; perhaps this means to revert back to your childhood psychologically. This defense mechanism is less common. Rationalization is the use of seemingly logical explanations to explain away the painful truth. For example, a woman who has been abused by her husband may think that if she only prepared a better meal, this wouldn’t have happened. Denial is lying to oneself. You simply say it isn’t so. “He won’t really leave.” Or “I’m not really in that much debt.” Sublimation involves transforming unacceptable urges (such as aggression or sexual urges) into acceptable behaviors such as exercise or competition. Displacement involves carrying out frustration onto a safer target. Have you ever been overly upset about something very simple? It may be a sign of displacing your frustration that is really about something else. Projection is the tendency to attribute your feelings onto others. So a person who is angry suggests that it is someone else who is really mad. Reaction formation involves outwardly opposing something inwardly desired, yet feared. A person who is rigidly opposed to something might really be fighting their own tendencies.
Freud’s theory of self suggests that there are three parts of the self.
The id is the part of the self that is inborn. It responds to biological urges without pause and is guided by the principle of pleasure: if it feels good, it is the thing to do. A newborn is all id. The newborn cries when hungry, defecates when the urge strikes. The ego develops through interaction with others and is guided by logic or the reality principle. It has the ability to delay gratification. It knows that urges have to be managed. It mediates between the id and superego using logic and reality to calm the other parts of the self. The superego represents society’s demands for its members. It is guided by a sense of guilt. Values, morals, and the conscience are all part of the superego.
The personality is thought to development in response to the child’s ability to learn to manage biological urges. Parenting is important here. If the parent is either overly punitive or lax, the child may not progress to the next stage. The oral stage lasts from birth until around age 2. The infant is all id. At this stage, all stimulation and comfort is focused on the mouth and is based on the reflex of sucking. Too much indulgence or too little stimulation may lead to fixation. The anal stage coincides with potty training or learning to manage biological urges. The ego is beginning to develop in this stage. Anal fixation may result in a person who is compulsively clean and organized or one who is sloppy and lacks self-control. The phallic stage occurs in early childhood and marks the development of the superego and a sense of masculinity or femininity as culture dictates. Latency occurs during middle childhood when a child’s urges quiet down and friendships become the focus. The ego and superego can be refined as the child learns how to cooperate and negotiate with others. The genital stage begins with puberty and continues through adulthood. Now the preoccupation is that of sex and reproduction.
Freud focused on biology as a prime motivator. Erikson suggested that our relationships and society’s expectations motivate much of our behavior in his theory of psychosocial development. Erikson was a student of Freud’s but emphasized the importance of the ego, or conscious thought, in determining our actions. In other words, he believed that we are not driven by unconscious urges. We know what motivates us and we consciously think about how to achieve our goals. He is considered the father of developmental psychology because his model gives us a guideline for the entire life span and suggests certain primary psychological and social concerns throughout life.
Erikson’s first four stages address childhood. Each stage is an elaboration of the previous stage. So, for example, a sense of trust in infancy can extend to a sense of autonomy in toddlerhood. Trust versus mistrust is the crisis of infancy. The infant is dependent and hopes that needs are met. If so, the infant may gain a sense that the world is a trustworthy place. Autonomy (or self-rule) versus shame and doubt is the struggle of toddlers. Once the toddler can walk and talk, he wonders where he can go and what can be said. The ability to be independent within safe limits is the goal. Initiative versus guilt guides early childhood. The child wants to plan and begin a task or project without assistance. Maybe it’s building a fort out of all the couch cushions or putting together a play and making paper tickets. (Keep in mind that the couch cushions won’t necessarily be picked up right away. After all, the goal is initiation, not completion!) Industry versus inferiority is the primary concern once a child is learning how to get along with other children and begins participating in school or other endeavors in which children come together and are compared. Industry involves being very busy and trying out one’s skills. Hopefully, the child has successes and believes that they measure up well when comparisons are made.
The last four stages address adolescence and continue through life. Adolescents struggle with identity . Teenagers struggle with the question, “Who am I?” Who am I socially, physically, sexually, morally, academically, and so on? The early adult is focused on intimacy versus isolation . Once an identity has been established, the person is in a better position to make intimate, long-term commitments. Generativity or productivity and a sense of giving back to the next generation are a concern during midlife or much of adulthood. A person looks at their life and hopes to be doing something that is worthwhile. If not, they may feel stagnated or stuck and impelled to make changes. Integrity versus despair concerns us at the end of life. We want to look back and think that we have lived according to our beliefs. We want to see agreement between who we are and what we’ve done. If not, we may experience a sense of despair because time is running out.
Exercises
Now, test yourself.
Who is the father of developmental psychology?
According to Freud, which part of the self are we born with?
At what age do we establish a basic sense of trust, per Erikson?

When does the ego develop?
How would you test Freudian concepts? Well, that’s a hard question. The answer is probably, “with great difficulty.”
Learning theories explain some of the ways that experience changes what we are capable of doing. Unlike psychodynamic theories, learning theories focus on behaviors that are observable.
We are going to explore three theories: classical conditioning, operant conditioning, and social learning theory.
Classical conditioning is an explanation of how we learn to feel the way we do. Ivan Pavlov was a Russian physiologist who discovered that certain cues in our environment can create automatic physiological responses in us. For example, if you think of lemons, you may start to salivate and your mouth may pucker. The reason is because you’ve associated the word lemon with your experience when tasting a lemon. Now the word can bring about the same response. Classical conditioning occurs when we learn through association. The reaction is a gut level, physiological response like heart rate, relaxation, respiration and other ways that our body changes when experiencing an emotion. Our sympathetic and parasympathetic divisions of the autonomic nervous system are engaged.
Pavlov’s understanding of classical conditioning developed out of his work when studying how saliva breaks down food. Notice that this dog has a tube attached to his mouth. This is designed to capture saliva that can be measured when the dog is eating. Pavlov noticed that the dogs produced saliva even before he introduced food. For example, they began to salivate when they heard his assistant coming down the hall. Why? Because they knew that footsteps come before food and therefore their bodies are getting ready to digest by producing salivation. Salivating to footsteps is a response to a psychological event or thought process. Pavlov called this a “psychic reflex” and began to pair other stimuli to feeding. For example, he rang a bell just before feeding. After that pairing was made several times, the dog would then begin to salivate to the bell.
Let’s review some terms by applying these to the experiment just described. Before conditioning has occurred, we see that dogs naturally produce saliva when food is introduced. The unconditioned stimulus is food and the unconditioned response is salivation. After the bell has become associated with food, the dog begins to salivate when hearing the bell. The conditioned (or learned) stimulus is now the sound of the bell. The conditioned (or learned) response is to salivate to the sound of the bell.
Let’s take this information beyond dogs and salivation.
John B. Watson built upon Pavlov’s work by applying the principles of classical conditioning to children. He was considered a parenting expert in the 1920s and wrote a column in the newspaper giving parenting advice. He rejected the idea that genetics explained our actions. Rather, he thought that learning was key in determining how children behave. Consequently, he emphasized the importance of parenting practices. He believed that children could be taught to love or hate anything associate with unconditioned stimuli. He demonstrated this in his work with Little Albert by teaching Albert to be afraid of a variety of animals and other objects after they had been associated with a loud noise, which Albert automatically feared.
Watson left academia and carried his message to the world of advertising. One of his first clients was Sunkist, a company who sold oranges. Watson created an ad in which a beautiful woman was shown holding an orange. Think about this example and identify the unconditioned stimulus, the unconditioned response, the conditioned stimulus, and the conditioned response for review.
Now let’s turn our attention to operant conditioning . This is an explanation of why we repeat voluntary actions or operants. For example, demonstrate a voluntary action right now as you’re working through this lesson. What did you do? Perhaps you raised your hand or looked up. Maybe you decided to stand or say something. All of these are operants. Now, if I wanted to encourage you to do this again, how would I go about it? Maybe asking you to do it again would be sufficient. But chances are I would need to make it rewarding in order to get you to repeat that action.
The Law of Effect states that an organism will repeat an action if it is followed by a good effect. If I were with you now, I might be able to smile when you stood up and therefore increase the likelihood that you would stand again.
Reinforcement encourages a behavior. B. F. Skinner, who brought us the principles of operant conditioning, suggested that reinforcement is a more effective means of encouraging a behavior than is criticism or punishment. By focusing on strengthening desirable behavior, we have a greater impact than if we emphasize what is undesirable. Reinforcement is anything that an organism desires and is motivated to obtain. A reinforcer is something that encourages or promotes a behavior. Some things are natural rewards . They are considered intrinsic or primary because their value is easily understood. Think of what kinds of things babies or animals such as puppies find rewarding.
Extrinsic or secondary reinforcers are things that have a value not immediately understood. Their value is indirect. They can be traded in for what is ultimately desired.
The use of positive reinforcement involves adding something to a situation in order to encourage a behavior. For example, if I give a child a cookie for cleaning a room, the addition of the cookie makes cleaning more likely in the future. Think of ways in which you positively reinforce others.
Negative reinforcement occurs when taking something unpleasant away from a situation encourages behavior. For example, I have an alarm clock that makes a very unpleasant, loud sound when it goes off in the morning. As a result, I get up and turn it off. By removing the noise, I am reinforced for getting up. How do you negatively reinforce others?
Punishment is an effort to stop a behavior. It means to follow an action with something unpleasant or painful. Punishment is often less effective than reinforcement for several reasons. It doesn’t indicate the desired behavior, it may result in suppressing rather than stopping a behavior, (in other words, the person may not do what is being punished when you’re around, but may do it often when you leave), and a focus on punishment can result in not noticing when the person does well.
Not all behaviors are learned through association or reinforcement. Many of the things we do are learned by watching others. This is addressed in social learning theory.
Social learning theory occurs when we copy, imitate, or learn a role by watching other people. Others include family members, friends, as well as role models in the media. We use modeling as a quick guide to tell us how to act particularly when we are in new situations. Perhaps you’ve started a new job or become a parent. One of the ways to learn how to behave in these situations is to witness someone else in this role and use them as a guide. Review the commentary from Albert Bandura in the video clip of the Bobo Doll experiment contained in your lesson. Notice that modeling is more than copying or imitating. It involves creating new ways to act out a role. The children demonstrate new aggressive behavior never seen in the model.
Cognitive theories of development explain how our ability to think changes over time. Our thoughts and reasoning abilities differ when we are 6 or 16 or 36 years of age. Let’s explore how and why this change occurs. We will focus on two theorists: Piaget and Vygotsky.
Jean Jacque Piagetis considered the father of cognitive psychology. He offered a theory of how our ability to make sense of the world changes as we mature.
Our desire to understand the world comes from a need for cognitive equilibrium. This is an agreement or balance between what we sense in the outside world and what we know in our minds. If we experience something that we cannot understand, we try to restore the balance by either changing our thoughts or by altering the experience to fit into what we do understand. Perhaps you meet someone who is very different from anyone you know. How do you make sense of this person? You might use them to establish a new category of people in your mind or you might think about how they are similar to someone else.
A schema or schemes are categories of knowledge. They are like mental boxes of concepts. A child has to learn many concepts. They may have a scheme for “under” and “soft” or “running” and “sour”. All of these are schema. Our efforts to understand the world around us lead us to develop new schema and to modify old ones.
One way to make sense of new experiences is to focus on how they are similar to what we already know. So the person we meet who is very different may be understood as being “sort of like my brother” or “his voice sounds a lot like yours.” Or a new food may be assimilated when we determine that it tastes like chicken! This is assimilation .
Another way to make sense of the world is to change our mind. We can make a cognitive accommodation to this new experience by adding new schema. This food is unlike anything I’ve tasted before. I now have a new category of foods that are bitter-sweet in flavor, for instance. This is accommodation . Do you accommodate or assimilate more frequently? Children accommodate more frequently as they build new schema. Adults tend to look for similarity in their experience and assimilate. They may be less inclined to think “outside the box.”
Piaget suggested different intelligences or ways of understanding that are associated with maturation.
- Sensorimotor intelligence is based on knowledge that relies on use of the senses and motor skills. From birth until about age 2, the infant knows by tasting, smelling, touching, hearing, and moving objects around. This is a real hands on type of knowledge.
- Preoperational intelligence involves being able to think about the world using symbols. A symbol is something that stands for something else. The use of language, whether it is in the form of words or gestures, facilitates knowing and communicating about the world. This is the hallmark of preoperational intelligence and occurs in early childhood. However, these children are preoperational or pre-logical. They still do not understand how the physical world operates.
- Concrete operational intelligence is the ability to think logically about the physical world. Middle childhood is a time of understanding concepts such as size, distance, and constancy of matter, and cause and effect relationships. A child knows that a scrambled egg is still an egg and that 8 ounces of water is still 8 ounces no matter what shape of glass contains it.
- Formal operational intelligence is the ability to think logically about concrete and abstract events. The teenager who has reached this stage is able to consider possibilities and to contemplate ideas about situations that have never been directly encountered. More abstract understanding of religious ideas or morals or ethics and abstract principles such as freedom and dignity can be considered.
Lev Vygotsky was a Russian psychologist who focused on the process of guidance and interaction that occurs in all cultures when teaching cognitive skills. He believed that cognitive abilities were not entirely dependent on physical maturation. Cognitive abilities are acquired through guidance and interaction with others. This interaction involves scaffolding in which the child or apprentice in learning is given hands-on assistance along with explanation as they learn to perform a task. The key is to work with a child within their zone of proximal development. The task needs to be stimulating enough to engage their learning but not too difficult to achieve.
One of the most comprehensive theories of human development comes to us from Urie Bronfenbrenner. Bronfenbrenner studies Freud, Erikson, Piaget, and learning theorists and believed that all of those theories could be enhanced by adding the dimension of context.
Bronfenbrenner’s model explains the direct and indirect influences on an individual’s development.  These are the people with whom the child interacts such as parents, peers, and teachers. The relationship between individuals and those around them need to be considered. For example, to appreciate what is going on with a student in math, the relationship between the student and teacher should be known. Mesosystems are interactions between those surrounding the individual. The relationship between parents and schools, for example will indirectly affect the child. Larger institutions such as the mass media or the healthcare system are referred to as the exosystem. These have an impact on families and peers and schools who operate under policies and regulations found in these institutions. We find cultural values and beliefs at the level of macrosystems. These larger ideals and expectations inform institutions that will ultimately impact the individual.
All of this happens in an historic context referred to as the chronosystem . Cultural values change over time as do policies of educational institutions or governments in certain political climates. Development occurs at a point in time.
So in order to understand a student in math, we can’t simply look at that individual and what challenges they face directly with the subject. We have to look at the interactions that occur between teacher and child. Perhaps the teacher needs to make modifications as well. The teacher may be responding to regulations made by the school such as new expectations for students in math or constraints on time that interfere with the teacher’s ability to instruct. These new demands may be a response to national efforts to promote math and science deemed important by a political leaders in response to relations with other countries at a particular time in history.
In sum, this model challenges us to go beyond the individual if we want to understand human development and promote improvements.


1.1: Introduction
(Credit: Steve Bowbrick/ flickr/ Attribution 2.0 Generic (CC BY 2.0))
So, you’re in this course and you may have pondered, or discussed with others, what this course will be about. You probably have some preconceptions of what management is all about. You must manage your time, deciding on how much study time you will devote to your management and accounting classes, for instance. You may have had a summer or part-time job where you had a manager whom you had to report to. You may have followed news reports on successful managers like Jeff Bezos of Amazon or Sheryl Sandberg of Facebook and want to learn what made them successful so you can emulate their practices in your business career. You may have the impression (not an accurate one) that management is basically just common sense and that you really don’t need to take this course except that you must meet your degree requirement.
You may be an accounting or marketing major who is taking this class because it is required for completion of your degree requirements, but you don’t think that you will ever require what you learn in this class during your career since you don’t plan on applying for HR jobs upon graduation. If you’re believing this, you could not be more mistaken. Regardless of where you are in your career, be it as an individual contributor, project leader, or middle or senior manager, what you will get out of this course will be valuable. If your first job out of college is as an accountant, sales representative, or another entry-level position, you will appreciate the roles that your managers, both direct and senior level, play in an organization and the behaviors and actions that will get you recognized and appreciated. Best of luck!
Most management textbooks would say, as does this one, that managers spend their time engaged in planning, organizing, staffing, directing, coordinating, reporting, and controlling. These activities, as Hannaway found in her study of managers at work, “do not, in fact, describe what managers do.” 1 At best they seem to describe vague objectives that managers are continually trying to accomplish. The real world, however, is far from being that simple. The world in which most managers work is a “messy and hectic stream of ongoing activity." 2
References
- Hannaway, J. (1989 ). Managers Managing: The Workings of an Administrative System . New York: Oxford University Press, P. 39.
- Eccles, R. G. & Nohria, N. (1992). Beyond the Hype: Rediscovering the Essence of Management . Boston: The Harvard Business School Press, p. 47.


2.2: Scalars and Vectors (Part 1)
- Describe the difference between vector and scalar quantities.
- Identify the magnitude and direction of a vector.
- Explain the effect of multiplying a vector quantity by a scalar.
- Describe how one-dimensional vector quantities are added or subtracted.
- Explain the geometric construction for the addition or subtraction of vectors in a plane.
- Distinguish between a vector equation and a scalar equation.
Many familiar physical quantities can be specified completely by giving a single number and the appropriate unit. For example, “a class period lasts 50 min” or “the gas tank in my car holds 65 L” or “the distance between two posts is 100 m.” A physical quantity that can be specified completely in this manner is called a scalar quantity . Scalar is a synonym of “number.” Time, mass, distance, length, volume, temperature, and energy are examples of scalar quantities.
Scalar quantities that have the same physical units can be added or subtracted according to the usual rules of algebra for numbers. For example, a class ending 10 min earlier than 50 min lasts 50 min − 10 min = 40 min. Similarly, a 60-cal serving of corn followed by a 200-cal serving of donuts gives 60 cal + 200 cal = 260 cal of energy. When we multiply a scalar quantity by a number, we obtain the same scalar quantity but with a larger (or smaller) value. For example, if yesterday’s breakfast had 200 cal of energy and today’s breakfast has four times as much energy as it had yesterday, then today’s breakfast has 4(200 cal) = 800 cal of energy. Two scalar quantities can also be multiplied or divided by each other to form a derived scalar quantity. For example, if a train covers a distance of 100 km in 1.0 h, its speed is 100.0 km/1.0 h = 27.8 m/s, where the speed is a derived scalar quantity obtained by dividing distance by time.
Many physical quantities, however, cannot be described completely by just a single number of physical units. For example, when the U.S. Coast Guard dispatches a ship or a helicopter for a rescue mission, the rescue team must know not only the distance to the distress signal, but also the direction from which the signal is coming so they can get to its origin as quickly as possible. Physical quantities specified completely by giving a number of units (magnitude) and a direction are called vector quantities . Examples of vector quantities include displacement, velocity, position, force, and torque. In the language of mathematics, physical vector quantities are represented by mathematical objects called vectors (Figure \(\PageIndex{1}\)). We can add or subtract two vectors, and we can multiply a vector by a scalar or by another vector, but we cannot divide by a vector. The operation of division by a vector is not defined.
Let’s examine vector algebra using a graphical method to be aware of basic terms and to develop a qualitative understanding. In practice, however, when it comes to solving physics problems, we use analytical methods, which we’ll see in the next section. Analytical methods are more simple computationally and more accurate than graphical methods. From now on, to distinguish between a vector and a scalar quantity, we adopt the common convention that a letter in bold type with an arrow above it denotes a vector, and a letter without an arrow denotes a scalar. For example, a distance of 2.0 km, which is a scalar quantity, is denoted by d = 2.0 km, whereas a displacement of 2.0 km in some direction, which is a vector quantity, is denoted by \(\vec{d}\).
Suppose you tell a friend on a camping trip that you have discovered a terrific fishing hole 6 km from your tent. It is unlikely your friend would be able to find the hole easily unless you also communicate the direction in which it can be found with respect to your campsite. You may say, for example, “Walk about 6 km northeast from my tent.” The key concept here is that you have to give not one but two pieces of information—namely, the distance or magnitude (6 km) and the direction (northeast).
Displacement is a general term used to describe a change in position, such as during a trip from the tent to the fishing hole. Displacement is an example of a vector quantity. If you walk from the tent (location A) to the hole (location B), as shown in Figure \(\PageIndex{2}\), the vector \(\vec{D}\), representing your displacement , is drawn as the arrow that originates at point A and ends at point B. The arrowhead marks the end of the vector. The direction of the displacement vector \(\vec{D}\) is the direction of the arrow. The length of the arrow represents the magnitude D of vector \(\vec{D}\). Here, D = 6 km. Since the magnitude of a vector is its length, which is a positive number, the magnitude is also indicated by placing the absolute value notation around the symbol that denotes the vector; so, we can write equivalently that D ≡ |\(\vec{D}\)|. To solve a vector problem graphically, we need to draw the vector \(\vec{D}\) to scale. For example, if we assume 1 unit of distance (1 km) is represented in the drawing by a line segment of length u = 2 cm, then the total displacement in this example is represented by a vector of length d = 6u = 6(2 cm) = 12 cm , as shown in Figure \(\PageIndex{3}\). Notice that here, to avoid confusion, we used D = 6 km to denote the magnitude of the actual displacement and d = 12 cm to denote the length of its representation in the drawing.
Suppose your friend walks from the campsite at A to the fishing pond at B and then walks back: from the fishing pond at B to the campsite at A. The magnitude of the displacement vector \(\vec{D}_{AB}\) from A to B is the same as the magnitude of the displacement vector \(\vec{D}_{BA}\) from B to A (it equals 6 km in both cases), so we can write \(\vec{D}_{AB}\) = \(\vec{D}_{BA}\). However, vector \(\vec{D}_{AB}\) is not equal to vector \(\vec{D}_{BA}\) because these two vectors have different directions: \(\vec{D}_{AB}\) ≠ \(\vec{D}_{BA}\). In Figure 2.3, vector \(\vec{D}_{BA}\) would be represented by a vector with an origin at point B and an end at point A, indicating vector \(\vec{D}_{BA}\) points to the southwest, which is exactly 180° opposite to the direction of vector \(\vec{D}_{AB}\). We say that vector \(\vec{D}_{BA}\) is antiparallel to vector \(\vec{D}_{AB}\) and write \(\vec{D}_{AB}\) = \(-\vec{D}_{BA}\), where the minus sign indicates the antiparallel direction.
Two vectors that have identical directions are said to be parallel vectors —meaning, they are parallel to each other. Two parallel vectors \(\vec{A}\) and \(\vec{B}\) are equal, denoted by \(\vec{A}\) = \(\vec{B}\), if and only if they have equal magnitudes |\(\vec{A}\)| = |\(\vec{B}\)|. Two vectors with directions perpendicular to each other are said to be orthogonal vectors . These relations between vectors are illustrated in Figure \(\PageIndex{4}\).
Two motorboats named Alice and Bob are moving on a lake. Given the information about their velocity vectors in each of the following situations, indicate whether their velocity vectors are equal or otherwise.
- Alice moves north at 6 knots and Bob moves west at 6 knots.
- Alice moves west at 6 knots and Bob moves west at 3 knots.
- Alice moves northeast at 6 knots and Bob moves south at 3 knots.
- Alice moves northeast at 6 knots and Bob moves southwest at 6 knots.
- Alice moves northeast at 2 knots and Bob moves closer to the shore northeast at 2 knots.
Algebra of Vectors in One Dimension
Vectors can be multiplied by scalars, added to other vectors, or subtracted from other vectors. We can illustrate these vector concepts using an example of the fishing trip seen in Figure \(\PageIndex{5}\).
Suppose your friend departs from point A (the campsite) and walks in the direction to point B (the fishing pond), but, along the way, stops to rest at some point C located three-quarters of the distance between A and B, beginning from point A (Figure \(\PageIndex{5a}\)). What is his displacement vector \(\vec{D}_{AC}\) when he reaches point C? We know that if he walks all the way to B, his displacement vector relative to A is \(\vec{D}_{AB}\), which has magnitude D AB = 6 km and a direction of northeast. If he walks only a 0.75 fraction of the total distance, maintaining the northeasterly direction, at point C he must be 0.75 D AB = 4.5 km away from the campsite at A. So, his displacement vector at the rest point C has magnitude D AC = 4.5 km = 0.75 D AB and is parallel to the displacement vector \(\vec{D}_{AB}\). All of this can be stated succinctly in the form of the following vector equation :
\[\vec{D}_{AC} = 0.75\; \vec{D}_{AB} \ldotp \nonumber\]
In a vector equation, both sides of the equation are vectors. The previous equation is an example of a vector multiplied by a positive scalar (number) \(\alpha\) = 0.75. The result, \(\vec{D}_{AC}\), of such a multiplication is a new vector with a direction parallel to the direction of the original vector \(\vec{D}_{AB}\). In general, when a vector \(\vec{D}_{A}\) is multiplied by a positive scalar \(\alpha\), the result is a new vector \(\vec{D}_{B}\) that is parallel to \(\vec{D}_{A}\):
\[\vec{B} = \alpha \vec{A} \label{2.1}\]
The magnitude |\(\vec{B}\)| of this new vector is obtained by multiplying the magnitude |\(\vec{A}\)| of the original vector, as expressed by the scalar equation :
\[ B = | \alpha | A \ldotp \label{2.2}\]
In a scalar equation, both sides of the equation are numbers. Equation \ref{2.2} is a scalar equation because the magnitudes of vectors are scalar quantities (and positive numbers). If the scalar \(\alpha\) is negative in the vector equation Equation \ref{2.1}, then the magnitude |\(\vec{B}\)| of the new vector is still given by Equation \ref{2.2}, but the direction of the new vector \(\vec{B}\) is antiparallel to the direction of \(\vec{A}\). These principles are illustrated in Figure \(\PageIndex{6a}\) by two examples where the length of vector \(\vec{A}\) is 1.5 units. When \(\alpha\) = 2, the new vector \(\vec{B}\) = 2\(\vec{A}\) has length B = 2A = 3.0 units (twice as long as the original vector) and is parallel to the original vector. When \(\alpha\) = −2, the new vector \(\vec{C}\) = −2\(\vec{A}\) has length C = |−2| A = 3.0 units (twice as long as the original vector) and is antiparallel to the original vector.
Now suppose your fishing buddy departs from point A (the campsite), walking in the direction to point B (the fishing hole), but he realizes he lost his tackle box when he stopped to rest at point C (located three-quarters of the distance between A and B, beginning from point A). So, he turns back and retraces his steps in the direction toward the campsite and finds the box lying on the path at some point D only 1.2 km away from point C (see Figure \(\PageIndex{5b}\)). What is his displacement vector \(\vec{D}_{AD}\) when he finds the box at point D? What is his displacement vector \(\vec{D}_{DB}\) from point D to the hole? We have already established that at rest point C his displacement vector is \(\vec{D}_{AC}\) = 0.75 \(\vec{D}_{AB}\). Starting at point C, he walks southwest (toward the campsite), which means his new displacement vector \(\vec{D}_{CD}\) from point C to point D is antiparallel to \(\vec{D}_{AB}\). Its magnitude |\(\vec{D}_{CD}\)| is D CD = 1.2 km = 0.2 D AB , so his second displacement vector is \(\vec{D}_{CD}\) = −0.2 \(\vec{D}_{AB}\). His total displacement \(\vec{D}_{AD}\) relative to the campsite is the vector sum of the two displacement vectors: vector \(\vec{D}_{AC}\) (from the campsite to the rest point) and vector \(\vec{D}_{CD}\) (from the rest point to the point where he finds his box):
\[\vec{D}_{AD} = \vec{D}_{AC} + \vec{D}_{CD} \ldotp \label{2.3}\]
The vector sum of two (or more vectors is called the resultant vector or, for short, the resultant . When the vectors on the right-hand-side of Equation \ref{2.3} are known, we can find the resultant \(\vec{D}_{AD}\) as follows:
\[\vec{D}_{AD} = \vec{D}_{AC} + \vec{D}_{CD} = 0.75\; \vec{D}_{AB} - 0.2\; \vec{D}_{AB} = (0.75 - 0.2) \vec{D}_{AB} = 0.55 \vec{D}_{AB} \ldotp \label{2.4}\]
When your friend finally reaches the pond at B, his displacement vector \(\vec{D}_{AB}\) from point A is the vector sum of his displacement vector \(\vec{D}_{AD}\) from point A to point D and his displacement vector \(\vec{D}_{DB}\) from point D to the fishing hole: \(\vec{D}_{AB}\) = \(\vec{D}_{AD}\) + \(\vec{D}_{DB}\) (see Figure \(\PageIndex{5c}\)). This means his displacement vector \(\vec{D}_{DB}\) is the difference of two vectors:
\[\vec{D}_{DB} = \vec{D}_{AB} − \vec{D}_{AD} = \vec{D}_{AB} + (− \vec{D}_{AD}) \ldotp \label{2.5}\]
Notice that a difference of two vectors is nothing more than a vector sum of two vectors because the second term in Equation \ref{2.5} is vector \(- \vec{D}_{AD}\) (which is antiparallel to \(\vec{D}_{AD}\)). When we substitute Equation \ref{2.4} into Equation \ref{2.5}, we obtain the second displacement vector:
\[\vec{D}_{DB} = \vec{D}_{AB} − \vec{D}_{AD} = \vec{D}_{AB} − 0.55\; \vec{D}_{AB} = (1.0 − 0.55)\; \vec{D}_{AB} = 0.45\; \vec{D}_{AB} \ldotp \label{2.6}\]
This result means your friend walked D DB = 0.45 D AB = 0.45(6.0 km) = 2.7 km from the point where he finds his tackle box to the fishing hole.
When vectors \(\vec{A}\) and \(\vec{B}\) lie along a line (that is, in one dimension), such as in the camping example, their resultant \(\vec{R}\) = \(\vec{A}\) + \(\vec{B}\) and their difference \(\vec{D}\) = \(\vec{A}\) − \(\vec{B}\) both lie along the same direction. We can illustrate the addition or subtraction of vectors by drawing the corresponding vectors to scale in one dimension, as shown in Figure \(\PageIndex{6}\).
To illustrate the resultant when \(\vec{A}\) and \(\vec{B}\) are two parallel vectors, we draw them along one line by placing the origin of one vector at the end of the other vector in head-to-tail fashion (see Figure (\PageIndex{6b}\)). The magnitude of this resultant is the sum of their magnitudes: R = A + B. The direction of the resultant is parallel to both vectors. When vector \(\vec{A}\) is antiparallel to vector \(\vec{B}\), we draw them along one line in either head-to-head fashion (Figure (\PageIndex{6c}\)) or tail-to-tail fashion. The magnitude of the vector difference, then, is the absolute value D = |A − B| of the difference of their magnitudes. The direction of the difference vector \(\vec{D}\) is parallel to the direction of the longer vector.
In general, in one dimension—as well as in higher dimensions, such as in a plane or in space—we can add any number of vectors and we can do so in any order because the addition of vectors is commutative ,
\[\vec{A} + \vec{B} = \vec{B} + \vec{A} \ldotp \label{2.7}\]
and associative,
\[ (\vec{A} + \vec{B}) + \vec{C} = \vec{A} + (\vec{B} + \vec{C}) \ldotp \label{2.8}\]
Moreover, multiplication by a scalar is distributive :
\[ \alpha_{1} \vec{A} + \alpha_{2} \vec{A} = (\alpha_{1} + \alpha_{2}) \vec{A} \ldotp \label{2.9}\]
We used the distributive property in Equation \ref{2.4} and Equation \ref{2.6}.
When adding many vectors in one dimension, it is convenient to use the concept of a unit vector . A unit vector, which is denoted by a letter symbol with a hat, such as \(\hat{u}\), has a magnitude of one and does not have any physical unit so that |\(\hat{u}\)| ≡ u = 1. The only role of a unit vector is to specify direction. For example, instead of saying vector \(\vec{D}_{AB}\) has a magnitude of 6.0 km and a direction of northeast, we can introduce a unit vector \(\hat{u}\) that points to the northeast and say succinctly that \(\vec{D}_{AB}\) = (6.0 km) \(\hat{u}\). Then the southwesterly direction is simply given by the unit vector\(- \hat{u}\). In this way, the displacement of 6.0 km in the southwesterly direction is expressed by the vector
\[\vec{D}_{BA} = (−6.0\; km)\; \hat{u} \ldotp \nonumber\]


23.6.1: Review Questions
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Review Questions
1 .
A new parent asks the nurse why the 36-hour-old newborn has a yellow skin tint. What should the nurse explain to the parent?
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The newborn’s liver is not functioning as well as it should.
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The yellow color indicates possible brain damage.
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The infant’s bowels are not excreting bilirubin.
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The color is a sign of physiologic jaundice, a normal finding.
2 .
At birth, a newborn weighed 6 pounds, 12 ounces. Three days later, the newborn weighs 5 pounds, 10 ounces. What conclusion should the nurse draw regarding this newborn’s weight?
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This weight loss is within normal limits.
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This weight gain is within normal limits.
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This weight loss is excessive.
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This weight gain is excessive.
3 .
The nurse is completing an initial assessment of the newborn. The newborn’s ears appear to be parallel to the outer and inner canthus of the eye. How does the nurse document the ear placement?
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low set
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high set
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a normal position
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facial paralysis
4 .
A new parent is concerned about a mass on the newborn’s head. The nurse assesses this to be a cephalohematoma based on what characteristics?
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The mass just appeared.
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The mass is on one side of the head and does not cross suture lines.
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The head is boggy and the crosses suture lines.
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The mass increases when the infant cries.
5 .
What condition can result from a long, difficult labor and is characterized by a localized, soft area on the newborn’s head?
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caput succedaneum
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molding
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depressed fontanelles
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cephalohematoma
6 .
During an assessment of a 12-hour-old newborn, the nurse notices pale pink spots on the nape of the neck. How does the nurse document this finding?
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nevus vasculosus
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Mongolian spots
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nevus flammeus
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telangiectatic nevi
7 .
How would the nurse elicit a rooting reflex in a newborn?
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Gently rub a finger on the side of the newborn’s cheek.
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Put a finger into the palm of the newborn’s hand and wait for them to grab on.

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Grab both arms, pulling upward, and let them go, watching for a startle response bilaterally.
8 .
The nurse notices that a 6-hour-old newborn patient’s urethral opening is on the dorsal side of the penis. The nurse knows that this is called what?
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hypospadias
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epispadias
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phimosis
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unispadias
9 .
The nurse is completing a gestational assessment on a newborn whose parent was treated for preeclampsia during labor. The neonate is demonstrating “frog-like” posturing. The nurse knows this is likely due to what medication during labor?
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fentanyl in the epidural
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penicillin for treatment of group B strep infection
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magnesium sulfate for treatment of preeclampsia
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prenatal vitamins
10 .
The nurse knows that a full-term newborn presents with ears that include what assessment characteristics?
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slightly curved pinna; soft; slow recoil
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well-curved pinna; soft; ready recoil
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thick cartilage, ear stiff
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pinna flat, stay folded
11 .
The nurse is assessing a newborn girl born at 40 weeks of gestation based on the parent’s LMP. What assessment finding of the genitalia confirms this gestational age?
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labia majora covering clitoris and labia minora
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clitoris prominent, labia minora enlarged
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small labia minora, clitoris enlarged
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labia majora enlarged, labia minora small
12 .
What are the characteristics of a 40-week preterm newborn male’s genitalia?
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scrotum empty, faint rugae
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testes in upper canal, rare rugae
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testes down, appropriate rugae
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testes pendulous, deep rugae
13 .
When assessing the newborn for the presence of lanugo, where should the nurse look for it?
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on the newborn’s face
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on the newborn’s extremities
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on the newborn’s back near their buttocks
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on the newborn’s back between the scapulae
14 .
The nurse is assigned to the postpartum room of a 12-hour-old neonate, and the EHR has a task reminder prompting the nurse to complete a Brazelton assessment on the newborn. Why is this not appropriate?
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This newborn has been born to a person who is placing the infant up for adoption.
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This newborn has been born to a person who birthed by cesarean section.
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This newborn is only 12 hours old.
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This newborn is experiencing pathologic jaundice.
15 .
The nurse is assigned to the room of a 15-year-old person who gave birth to a newborn 72 hours ago. Why is this newborn a perfect candidate for the Brazelton assessment?
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This parent-newborn couplet is at risk for delayed attachment.
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The newborn is likely going home soon.
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The EHR is prompting her to do so.
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The infant is likely withdrawing from a substance.
16 .
What categories are in the Brazelton assessment? Select all that apply.
- interactive process
- organizational process
- behavioral process
- motoric process
17 .
The nurse knows that during the interactive process of the Brazelton assessment, the newborn will receive an exceptionally good rating by reacting to what? Select all that apply.
- turns their head toward a familiar voice
- stays awake
- focuses on an object
- cries inconsolably
18 .
The nurse knows that during the motoric process, the newborn will be rated poorly if they do what?
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They have good reflexes.
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They have hyper- or hypotonic movements.
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They have good head control.
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They have moderate activity levels.
19 .
The nurse knows that during the organizational process, the newborn will be rated as exceptionally good if they do what? Select all that apply.
- They will remain alert.
- They will be highly irritable and demonstrate mood swings.
- They will demonstrate self-soothing and quieting techniques.
- The newborn will shut down body responses to stimuli when drowsy.
20 .
The nurse knows that newborns that are high-risk for delayed attachment with their parents/caregivers are at risk for what? Select all that apply.
- poor breast-feeding initiation
- not bonding with their parents
- hard to wake to feed
- not feeling happy
21 .
When the nurse determines they have a high-risk newborn and birthing person in their care, what can they do to mitigate the situation?
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Document in the chart.
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Reassure the parent that everything will be fine.
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Refer the couplet to social work for early intervention.
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Refer to a pediatric health-care provider for well-baby checkup.


4.2: Occupational Exposures
Occupational Noise Exposure
Sound levels
When employees are subjected to sound levels exceeding those listed in Table D-2, feasible administrative or engineering controls shall be utilized. If such controls fail to reduce sound levels measure in decibels (dBA) within the levels of the table, personal protective equipment as required in Subpart E, shall be provided and used to reduce sound levels within the levels of the table.
Tabe D-2 - Permissible Noise Exposures
|
Duration per day(hours) |
Sound Level dBA slow response |
|---|---|
|
8 |
90 |
|
6 |
92 |
|
4 |
95 |
|
3 |
97 |
|
2 |
100 |
|
1 ½ |
102 |
|
1 |
105 |
|
½ |
110 |
|
¼ or less |
115 |
In all cases where the sound levels exceed the values shown in Table D-2, a continuing effective hearing conservation program shall be administered.
When the daily noise exposure is composed of two or more periods of noise exposure of different levels, their combined effect should be considered, rather than the individual effect of each. Exposure to impulsive or impact noise should not exceed 140 dB peak sound pressure level.
Non-ionizing Radiation
Qualified and trained employees
Only qualified and trained employees shall be assigned to install, adjust and operate laser equipment. Proof of qualification for the laser equipment operator shall be available and in the possession of the operator at all times.
Exposure level for eye protection
Employees, when working in areas in which a potential exposure to direct or reflected laser light greater than 0.005 Watts (5 milliwatts) exists, shall be provided with anti-laser eye protection devices as specified in Subpart E of this part.
Warning signs
Areas in which lasers are used shall be posted with standard laser warning placards.
Beam shutters or caps
Beam shutters or caps shall be utilized, or the laser turned off, when laser transmission is not actually required. When the laser is left unattended for a substantial period of time such as during lunch hour, overnight, or at change of shifts, the laser shall be turned off. The laser beam shall not be directed at employees.
Environmental (weather) conditions
When it is raining or snowing, or when there is dust or fog in the air, the operation of laser systems shall be prohibited where practicable; in any event, employees shall be kept out of range of the area of source and target during such weather conditions.
Employee exposure limits
Laser equipment shall bear a label to indicate maximum output. Employees shall not be exposed to light intensities above:
- Direct staring: 1 micro-watt per square centimeter;
- Incidental observing: 1 milli-watt per square centimeter;
- Diffused reflected light: 2½ watts per square centimeter.
- A laser unit in operation should be set up above the heads of the employees, when possible. Employees shall not be exposed to microwave power densities in excess of 10 milli-watts per square centimeter.


12.20: Reading- Define Channels of Distribution
Evolution of Channels of Distribution
As consumers, we take for granted that when we go to a supermarket the shelves will be filled with the products we want; when we are thirsty there will be a Coke machine or bar around the corner, and we count on being able to get online and find any product available for purchase and quick delivery. Of course, if we give it some thought, we realize that this magic is not a given and that hundreds of thousands of people plan, organize, and labor long hours to make this convenience available. It has not always been this way, and it is still not this way in many other parts of the world.
Looking back over time, the channel structure in primitive culture was virtually nonexistent. The family or tribal group was almost entirely self-sufficient. The group was composed of individuals who were both communal producers and consumers of whatever goods and services could be made available. As economies evolved, people began to specialize in some aspect of economic activity. They engaged in farming, hunting, or fishing, or some other basic craft. Eventually this specialized skill produced excess products, which they exchanged or traded for needed goods that had been produced by others. This exchange process or barter marked the beginning of formal channels of distribution. These early channels involved a series of exchanges between two parties who were producers of one product and consumers of the other.
With the growth of specialization, particularly industrial specialization, and with improvements in methods of transportation and communication, channels of distribution have become longer and more complex. Thus, corn grown in Illinois may be processed into corn chips in West Texas, which are then distributed throughout the United States. Or, turkeys raised in Virginia are sent to New York so that they can be shipped to supermarkets in Virginia. Channels do not always make sense.
The channel mechanism also operates for service products. In the case of medical care, the channel mechanism may consist of a local physician, specialists, hospitals, ambulances, laboratories, insurance companies, physical therapists, home care professionals, and so on. All of these individuals are interdependent and could not operate successfully without the cooperation and capabilities of all the others.
Based on this relationship, we define a channel of distribution , also called a marketing channel, as sets of interdependent organizations involved in the process of making a product or service available for use or consumption, as well as providing a payment mechanism for the provider.
This definition implies several important characteristics of the channel. First, the channel consists of organizations , some under the control of the producer and some outside the producer’s control. Yet all must be recognized, selected, and integrated into an efficient channel arrangement.
Second, the channel management process is continuous and requires continuous monitoring and reappraisal. The channel operates twenty-four hours a day and exists in an environment where change is the norm.
Finally, channels should have certain distribution objectives guiding their activities. The structure and management of the marketing channel is thus, in part, a function of a firm’s distribution objective. It’s also a part of the marketing objectives, especially the need to make an acceptable profit. Channels usually represent the largest costs in marketing a product.
Channel Flows
One traditional framework that has been used to express the channel mechanism is the concept of flow. These flows reflect the many linkages that tie channel members and other agencies together in the distribution of goods and services. From the perspective of the channel manager, there are five important flows.
- Product flow : the movement of the physical product from the manufacturer through all the parties who take physical possession of the product until it reaches the ultimate consumer
- Negotiation flow : the institutions that are associated with the actual exchange processes
- Ownership flow : the movement of title through the channel
- Information flow : the individuals who participate in the flow of information either up or down the channel
- Promotion flow : the flow of persuasive communication in the form of advertising, personal selling, sales promotion, and public relations
Monster Channel Flow
The figure below maps the channel flows for the Monster Energy drink (and many other energy drink brands). Why is Monster’s relationship with Coca-Cola so valuable? Every single flow passes through bottlers and distributors in order to arrive in supermarkets where the product will be available to consumers.
Coca-Cola explains the importance of the bottlers in the distribution network:
While many view our Company as simply “Coca-Cola,” our system operates through multiple local channels. Our Company manufactures and sells concentrates, beverage bases and syrups to bottling operations, owns the brands and is responsible for consumer brand marketing initiatives. Our bottling partners manufacture, package, merchandise and distribute the final branded beverages to our customers and vending partners, who then sell our products to consumers.
All bottling partners work closely with customers — grocery stores, restaurants, street vendors, convenience stores, movie theaters and amusement parks, among many others — to execute localized strategies developed in partnership with our Company. Customers then sell our products to consumers at a rate of more than 1.9 billion servings a day. [1]
Revisiting the channel flows we find that the bottlers and distributors play a role in each flow. Examples of the flows are listed below. Remember, while the consumer is the individual who eventually consumes the drink, the supermarkets, restaurants, and other outlets are Coca-Cola’s customers.
- Product flow: the bottlers receive and process the bases and syrups
- Negotiation flow: the bottlers buy concentrate, sell product and collect revenue from customers
- Ownership flow: distributors acquire the title of the syrups and own the product until it’s sold to supermarkets
- Information flow: bottlers communicate product options to customers and communicate demand and needs to Coca-Cola
- Promotion flow: bottlers communicate benefits and provide promotional materials to customers
Contributors and Attributions
- Monster Channel Flows. Provided by : Lumen Learning. License : CC BY: Attribution
- Revision and adaptation. Provided by : Lumen Learning. License : CC BY: Attribution
- Chapter 10, Chanel Concepts, Distributing the Product, from Introducing Marketing. Authored by : John Burnett. Provided by : Global Text. Located at : http://solr.bccampus.ca:8001/bcc/file/ddbe3343-9796-4801-a0cb-7af7b02e3191/1/Core%20Concepts%20of%20Marketing.pdf . License : CC BY: Attribution
- Channels of Grace. Authored by : Liam Moloney. Located at : https://www.flickr.com/photos/tir_na_nog/5244765107/ . License : CC BY: Attribution
- Monster Energy. Authored by : Mike Mozart. Located at : https://www.flickr.com/photos/jeepersmedia/13100200773/ . License : CC BY: Attribution


11.1: Persuasion Theories
The first two parts of this book have covered strategies and techniques for preparing to speak informatively to audiences. The final portion focuses on speaking to persuade. Whereas an informational speech seeks to impart new, unique, and innovative messages to an audience, persuasive speaking takes it a step further by attempting to influence audience members’ ways of thinking or motivate them to action. In this respect, the art of persuasion requires careful planning and strategic composition, as well as delivery, to succeed. This chapter will explain why some strategies work and why others fail, as well as cover tips for refining an audience analysis to work more efficiently for a persuasive presentation.
People use persuasion to influence another person’s values, beliefs, attitudes, or behaviors. When thinking about persuasion, note the difference between influence and power .
Note to Self
Persuading others is truly an art form, which, when wielded properly and ethically, wields a unique power of its own—the power of communication that can change the world, even if it only changes it one person at a time.


26.6B: Ovarian Cycle
The menstrual cycle is the physiological process that fertile women undergo for the purposes of reproduction and fertilization.
- Differentiate among the phases of the menstrual cycle
Key Points
- The ovarian cycle refers to the series of changes in the ovary during which the follicle matures, the ovum is shed, and the corpus luteum develops.
- The follicular phase describes the development of the follicle in response to follicle stimulation hormone ( FSH ). As luteinizing hormone ( LH ) and FSH levels increase they stimulate ovulation, or the release of a mature oocyte into the fallopian tubes.
- In the luteal phase, the corpus luteum forms on the ovary and secretes many hormones, most significantly progesterone, which makes the endometrium of the uterus ready for implantation of an embryo.
- If implantation does not occur, the corpus luteum will be degraded, resulting in menstruation.
- If implantation occurs the corpus luteum is maintained.
Key Terms
-
ischemic phase
: The final part of the secretory phase. The endometrium becomes
pale and arteries constrict due to lower hormone release by the disintegrating corpus
luteum. -
granulosa cells
: These cells produce
hormones and growth factors that interact with the oocyte during its
development. - menstrual cycle : The recurring cycle of physiological changes in the females of some animal species that is associated with reproductive fertility.
- luteal phase : The latter part of the menstrual cycle that occurs after ovulation, in which the corpus luteum secretes progesterone to prepare the endometrium for the implantation of an embryo.
- follicular phase : The phase of the estrous cycle that involves follicular maturation within the ovary and, controlled by the hormone estradiol.
The menstrual cycle is the scientific term for the physiological changes that occur in fertile women for the purpose of sexual reproduction.The menstrual cycle is controlled by the endocrine system and commonly divided into three phases: the follicular phase, ovulation, and the luteal phase. However, some sources define these phases as menstruation, proliferative phase, and secretory phase. Menstrual cycles are counted from the first day of menstrual bleeding.
The Follicular Phase
The follicular phase (or proliferative phase) is the phase of the menstrual cycle in humans and great apes during which follicles in the ovary mature, ending with ovulation. The main hormone controlling this stage is estradiol. During the follicular phase, follicle-stimulating hormone (FSH) is secreted by the anterior pituitary gland. FSH levels begin to rise in the last few days of the previous menstrual cycle and peak during the first week of the follicular phase. The rise in FSH levels recruits five to seven tertiary-stage ovarian follicles (also known as Graafian or antral follicles) for entry into the menstrual cycle. These follicles compete with each other for dominance.
FSH induces the proliferation of granulosa cells in the developing follicles and the expression of luteinizing hormone (LH) receptors on these granulosa cells. Two or three days before LH levels begin to increase, usually by day seven of the cycle, one or occasionally two of the recruited follicles emerges as dominant. Many endocrinologists believe that estrogen secretion of the dominant follicle increases to a level that indirectly lowers the levels of LH and FSH. This slowdown in LH and FSH production leads to the atresia (death) of most of the recruited follicles, though the dominant follicle continues to mature.
These high estrogen levels initiate the formation of a new layer of endometrium in the uterus. Crypts in the cervix are also stimulated to produce fertile cervical mucus that reduces the acidity of the vagina, creating a more hospitable environment for sperm. In addition, basal body temperature may lower slightly under the influence of high estrogen levels. Ovulation normally occurs 30 (± 2) hours after the beginning of the LH surge (when LH is first detectable in urine).
Ovulation
Ovulation is the phase in which a mature ovarian follicle ruptures and discharges an ovum (also known as an oocyte, female gamete, or egg). Ovulation also occurs in the estrous cycle of other female mammals, which differs in many fundamental ways from the menstrual cycle. The time immediately surrounding ovulation is referred to as the ovulatory phase or the periovulatory period.
The Luteal Phase
The luteal phase (or secretory phase) is the latter part of the menstrual or estrous cycle. It begins with the formation of the corpus luteum and ends in either pregnancy or luteolysis. The main hormone associated with this stage is progesterone, which is significantly higher during the luteal phase than in other phases of the cycle. Some sources define the end of the luteal phase as a distinct ischemic phase.
After ovulation, the pituitary hormones FSH and LH cause the remaining parts of the dominant follicle to transform into the corpus luteum. It continues to grow for some time after ovulation and produces significant amounts of hormones, particularly progesterone, and to a lesser extent, estrogen. Progesterone plays a vital role in making the endometrium receptive to implantation of the blastocyst and supportive of the early pregnancy. It also raises the woman’s basal body temperature. The hormones produced by the corpus luteum suppress production of the FSH and LH, causing the corpus luteum will atrophy. The death of the corpus luteum results in falling levels of progesterone and estrogen. This in turn causes increased levels of FSH, leading to recruitment of follicles for the next cycle. Continued drops in estrogen and progesterone levels trigger the end of the luteal phase, menstruation, and the beginning of the next cycle.
The loss of the corpus luteum can be prevented by implantation of an embryo. After implantation, human embryos produce human chorionic gonadotropin (hCG), which is structurally similar to LH and can preserve the corpus luteum. Because the hormone is unique to the embryo, most pregnancy tests look for the presence of hCG. If implantation occurs, the corpus luteum will continue to produce progesterone (and maintain high basal body temperatures) for eight to twelve weeks, after which the placenta takes over this function.
The ovarian cycle : The ovarian cycle is the series of changes that occur in the ovary during the menstrual cycle that cause maturation of a follicle, ovulation, and development of the corpus luteum.


9.11.2: Thought Questions
Thought Questions
One of the primary scientific objectives of the Apollo program was the return of lunar material. Why was this so important? What can be learned from samples? Are they still of value now?
22.
Apollo astronaut David Scott dropped a hammer and a feather together on the Moon, and both reached the ground at the same time. What are the two distinct advantages that this experiment on the Moon had over the same kind of experiment as performed by Galileo on Earth?
23.
Galileo thought the lunar maria might be seas of water. If you had no better telescope than the one he had, could you demonstrate that they are not composed of water?
24.
Why did it take so long for geologists to recognize that the lunar craters had an impact origin rather than a volcanic one?
25.
How might a crater made by the impact of a comet with the Moon differ from a crater made by the impact of an asteroid?
26.
Why are the lunar mountains smoothly rounded rather than having sharp, pointed peaks (as they were almost always depicted in science-fiction illustrations and films before the first lunar landings)?
27.
The lunar highlands have about ten times more craters in a given area than do the maria. Does this mean that the highlands are 10 times older? Explain your reasoning.
28.
At the end of the section on the lunar surface, your authors say that lunar night and day each last about two Earth weeks. After looking over the information in Earth, Moon, and Sky and this chapter about the motions of the Moon, can you explain why? (It helps to draw a diagram for yourself.)
29.
Give several reasons Mercury would be a particularly unpleasant place to build an astronomical observatory.
30.
If, in the remote future, we establish a base on Mercury, keeping track of time will be a challenge. Discuss how to define a year on Mercury, and the two ways to define a day. Can you come up with ways that humans raised on Earth might deal with time cycles on Mercury?
31.
The Moon has too little iron, Mercury too much. How can both of these anomalies be the result of giant impacts? Explain how the same process can yield such apparently contradictory results.


Section 1: Fruits
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Fruits available daily
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Frequently
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Ready to get started
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Fruit options include fresh, frozen, and/or fruit packed in Water or juice (not packed in light or heavy syrup)
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Ready to get started
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Fruit options are accessible to Children for self-serving
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Ready to get started
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All fruit names are introduced to the children prior to the meal or snack
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Ready to get started
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Fruit names are written and/or pictured near where children eat
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Adults caring for children (mg, assistants, etc.) model to children how to serve themselves and participate in family style dining
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Notes / Reflections:
Section 2: Vegetables
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Vegetables available daily
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Ready to get started
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Vegetable options include and/or labeled "reduced sodium" or “no salt added”
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Vegetables are available to children for self-serving
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Ready to get started
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All vegetable names are introduced to the children prior to the meal or snack
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Ready to get started
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Vegetable names are written and/or pictured near where children eat
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Ready to get started
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Adults caring for children (mg, assistants, etc.) model to children how to serve themselves and participate in family style dining
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Ready to get started
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Notes / Reflections:
Section 3: Beverages
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Fat free or 1% milk is provided daily for children
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Milk is available to children for self-serving
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Drinking water is available to children for self-serving
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If juice is served it is either 100% fruit or vegetable juice
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Ready to get started
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All beverage names are introduced to the children prior to the meal or snack
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Ready to get started
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Beverage names are written and/or pictured near where children eat
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Notes / Reflections:
Section 4: Menu Selections
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Menu boards featuring daily meals and snacks are available and visible near Where Children eat (e.g. classroom or space)
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The menu includes a variety of foods which consider cultural and ethnic preferences
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The menu is modified for children with food allergies / intolerances and children with disabilities
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A monthly menu is provided to all families and staff
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All beverage names are introduced to the children prior to the meal or snack
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A monthly nutrition and/or physical activity message is included on the monthly menu
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Notes / Reflections:
Section 4: ECE Providers Role During Meal/Snack Time
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Mealtime takes place at regular scheduled time and is part of the children daily routine.
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Adults caring for children have been trained and model appropriate mealtime behavior
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Adults caring for children turn off all visible screens, including televisions, tablets, phones, etc. During meal time an engaging conversation with the children
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Adults caring for children sit with children at the table during meal time
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Adults caring for caring for children discuss if children stomachs feel full before serving a second helping of food
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During meal time, adults caring for children encourage children to try new or less preferred foods
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A transition activity (e.g. Reading a book, coloring activity, listening to quiet music, etc.) is offered to children when they're done with their meal
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Notes / Reflections:
Action Plan
Based on your self-assessment, create an action plan. Tips for completing your action plan:
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Share ideas and planning with staff in your program to ensure clear expectations
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Determine how many steps you think it will take to achieve a goal;
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Define the steps and determine who is responsible for each step; and
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Set a time-line for the completion of a goal and dates by which each step should be complete.
Action Plan Worksheet
Start Date:
ECE Program Name:
Goal:
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Objective / Steps
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Actions Items (Child, Family, Program, Staff)
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Program Environment
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Program Policies
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Sample Objective Step
: Update menus over a 3 month period to integrate more fruits an vegetables
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Discuss these changes with the children and how they help them grow strong and healthy
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Update menu boards to share information about fresh fruits and vegetables.
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Include healthy eating as a required topic at family orientation
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Who is responsible?
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Program Staff
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Program Director, cook teachers
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Program Director
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Date
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June 1
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Objective Step
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Who is responsible?
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-
antihistamine
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medication that relieves allergy symptoms, including stuffy nose and watery eyes
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barotrauma
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trauma that occurs when the air pressure in the middle ear does not equalize with ambient pressure
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benign paroxysmal positional vertigo (BPPV)
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a condition of the inner ear where otoliths migrate into the inner ear fluid, causing a false sense of spinning
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cerumenolytic
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a medication that softens and loosens ear wax to ease removal
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cochlear nerve
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one of two bifurcated nerves branching from the vestibulocochlear nerve; it transmits signals from the cochlea to the temporal lobe in the brain so sound can be heard
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decongestant
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a medication that shrinks swollen blood vessels and tissues in the nose to reduce nasal congestion and aid in relieving ear congestion
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eardrum
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a thin flap that separates the external or outer ear and middle ear; it vibrates to sound, which initiates an intricate relay throughout the ear structures traversing from the bones of the middle ear to the inner ear’s cochlea where hearing occurs; also known as the tympanic membrane
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Eustachian tube
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connects the middle ear to the nasal-sinus cavity
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external auditory canal
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path from the external ear to the middle ear
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incus
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one of three small bones in the middle ear; it transmits vibrations from the malleus to the stapes
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malleus
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one of three small bones in the middle ear; it is located closest to the tympanic membrane and transmits auditory oscillations to the incus
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Ménière’s disease
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occurs when fluid accumulates in the inner ear, which can be triggered by allergies, head injury, migraine headache; or viral infection; characterized by vertigo and hearing loss
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ossicles
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three small bones in the middle ear, consisting of the malleus, incus, and stapes, that transmit oscillatory vibrations from one small bone to another; the stapes sends sound to the inner ear in a highly coordinated relay system
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otitis externa
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inflammation and/or infection of the external ear canal characterized by itchiness, pain, and a red ear canal
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otitis media
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an inflammation or infection of the middle ear; also known as swimmer’s ear
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otolith
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a calcium carbonate crystal that normally resides in the base of the semicircular canal that can dislodge into the semicircular canal fluid and lead to bouts of vertigo
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stapes
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one of three small bones in the middle ear; it moves fluid into the cochlea in the inner ear
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tinnitus
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an ear disorder characterized by ringing or other annoying sounds in the ear
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tympanic cavity
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an air-filled compartment separated from the external ear by the tympanic membrane; it communicates with the pharynx via the Eustachian tube
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vestibular nerve
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one of two bifurcated nerves branching from the vestibulocochlear nerve; it controls motion and position
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vestibulocochlear nerve
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the eighth cranial nerve, which transmits sound from the inner ear to the auditory cortex in the temporal lobe of the brain.


11.4: Challenges in Organizational Communication
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- Last updated
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As you continue your education in college, you’ll continue to understand the need to be prepared for a perpetually evolving, increasingly diverse, and unpredictable global workplace. The key to organizational success, both for you and the organizations with whom you are involved, is effective communication. As you have probably experienced in both your personal relationships and organizational relationships, communication is not always successful. If you have ever worked on a group project for one of your classes, you have likely experienced many of the communicative challenges organizations face in this increasingly fast-paced and global world.
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Case In Point
The YouTube video ‘ Inside the Colony ’ shows the system in which ants use to communicate and live. What are some things we can draw from their lives into daily lives using organizational communication? Write bullet points on your ideas and pick the top on to discuss in class. |
Ineffective communication can cause many problems that can impact relationships, productivity, job satisfaction, and morale as we interact in organizations. Gerald Goldhaber summarizes Osmo Wiio’s “laws” of communication that are good to remember as you interact in increasingly complex organizations. Wiio pessimistically warns that: 1) If communication can fail, it will fail, 2) If a message can be understood in different ways, it will be misunderstood in the manner that does the most damage, 3) The more communication there is, the more tricky it is for the communication to be successful, and 4) There is always someone who thinks they know better what you said than you do.
One of the greatest challenges facing organizations is the practice of ethics. Ethics are a basic code of conduct (morals) that individuals and groups use to assess whether something is right or wrong. How ethical are you as an organizational participant? Do you always make ethical personal and professional decisions? Have you ever withheld a bit of truth to lessen the impact of revealing the whole truth? What if you accidentally overhear that an individual who is up for a promotion has been stealing from the organization? Do you tell your boss? Or, on a greater scale, what if you discover that your organization is withholding vital information from consumers, or violating lawful practices?  When you write your resume, how accurately do you describe your work history? Each of these scenarios deals directly with ethical considerations and ethical communication.
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Case In Point
A good example of an ethical dilemma that occurs in the workplace happened to me when one of my co-workers, who is also my good friend, was putting down more hours on her time card than she was actually working. This upset me, because I worked the exact same amount of time as her, yet I was being paid much less. Because our boss was so busy all the time, she never noticed this unfair violation of lawful practices. I had to choose between remaining silent which would prevent my friend from getting in trouble, or speaking out against the injustice in order to sustain a fair workplace. -Anonymous Coworker |
Many organizations practice a climate of “survival of the fittest” as individuals scramble their way up the ladder of success at any cost. Comedian Jimmy Durante posited this advice: “Be nice to people on your way up because you might meet ‘em on your way down.” Obviously, not every organization has this type of cutthroat culture, but with an inherent hierarchy and imbalance of power, organizations are ripe for unethical behaviors. Because of the competitive nature of many business climates, and the push for profits, organizational and individual ethics are often tested.
Do organizations have a moral responsibility to act ethically outside of their capitalistic and legal obligations? “Since 1985, more than two-thirds of Fortune 500 firms have been convicted of serious crimes, ranging from fraud to the illegal dumping of hazardous waste” (Eisenberg & Goodall 337). The Chevron Corporation, the second largest oil company in the U.S., is just one example of an unethical organization. Tax evasion and several environmental infractions, including dumping over 18 billion gallons of toxic waste into the Amazon rainforest, are examples of their ethical behavior (Sandhu, 2012). Other unethical practices common in organizations include exploiting workers, tax loopholes, overbilling, and dumping toxins. Despite these unfortunate, immoral practices, all of us have an obligation to communicate ethically in all aspects of our lives, including organizations.
|
Case In Point
Thinking of this incident in ethical terms Kreps’ three principles of ethical communication are of relevance. He states ethical treatment should 1) Tell the truth, 2) Do no harm, and 3) Treat people justly. Has Hills, Inc. engaged in ethical communication? How could they have done so? |
Differences in perception and the failure to clarify communication can lead to miscommunication at interpersonal as well as organizational levels. Organizationally, communication failure occurs due to information overload, communication anxiety, unethical communication, bad timing, too little information, message distortion, lack of respect, insufficient information, minimal feedback, ineffective communication, and even disinterest or apathy. To be successful in our organizational environments, we need to be earnest participants, as well as active listeners, to ensure effective communication and mutual satisfaction. Organizations cannot successfully operate without effective communication at every level.
Future Directions
As with many other specializations in the field of Communication, the area of organizational communication is changing faster than organizations, individuals, and scholars can adapt. It is difficult for organizations to anticipate and keep in front of the changes they encounter. What worked during the industrial age may no longer be relevant in the 21st century. In fact, what worked ten years ago likely does not work today. A sense of urgency, a fast pace, inconsistency, information overload, regenerating technology, and constant change characterize the dynamic changes as organizations move from operating in the industrial age to the information age. When this book was first published, for example, iPhones were just coming on the market. We referred to cds, dvds, and palm pilots in the original text. That was only eight eight years ago, and now we don’t use many of those technologies. Miller identifies four elements of the changing landscape for organizations: 1) Organizations are becoming more global, 2) Images and identity are becoming increasingly important, 3) There is a shift to a more predominant service economy, and 4) The changing workforce is highlighted by the “disposable worker” (Conrad & Poole), downsizing, early retirement, and temporary workers.
As a result, new directions of research are emerging. These changes are forcing those of us in organizational communication to reexamine existing communicative practices relative to the changing dynamics of organizations. For example, can a person lead without any personal, face-to-face contact? How do organizational values impact ethics, and what is the attitude towards ethical communication in this increasingly competitive age? How should work-life issues such as working parents, affirmative action, and drug screening be handled? With increasing diversity in the workplace, what is the role of intercultural communication? In this age of elevated tensions, how do stress and emotions communicatively manifest themselves in the workplace? What is the impact of our social media postings on our work lives?
|
Organizational Communication Now
This article
is about leadership and their ability to be flexible in work place. “Today’s leaders face challenges related to business disruption, ambiguity, complexity, widely connected constituencies and how to communicate with multiple constituencies simultaneously”. This ties into how work is different now than it was 10 years ago.
|
Scholars are continuing to communicatively adapt and respond to the changing landscape in terms of what we teach, research, and practice. Expect to see a variety of approaches and distinctively unique research agendas that will likely highlight the ways in which you will spend your life working in organizations that are different from today.
Contributions and Affiliations
- Survey of Communication Study. Authored by : Scott T Paynton and Linda K Hahn. Provided by : Humboldt State University. Located at : en.wikibooks.org/wiki/Survey_of_Communication_Study/Preface. License : CC BY-SA: Attribution-ShareAlike


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4.5: Lecture Outline for Part III
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Last updated
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Save as PDF
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Suggested Lecture Material for Part III—Sex, Gender, and Sexual Orientation
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Identify and differentiate among sex, gender, and sexual orientation.
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Sex
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Gender
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Roles
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Sex-appropriate behavior
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The Looking Glass Self
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The Self-Fulfilling Prophecy
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Sexual Orientation-GLBT
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Straight Males
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Straight Females
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Gay (Males)
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Lesbian (Females)
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Bisexual
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Transgendered (Male to Female)
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Transgendered (Female to Male)
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Intersexed
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Use the Internet to display statistical information concerning sex, gender, and sexual orientation..
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Compare and contrast the data found.
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Use the Internet to display statistical information concerning the historical legal status of women in the United States.
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Use the Internet to display statistical information concerning the historical legal status of GLBTs in the United States.
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Define and give examples for:
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Gender identity
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Sex roles
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Masculinity
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Femininity
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Discuss the various forms that inequality based on sex takes around the world.
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Discuss the status of women in Kuwait and Saudi Arabia.
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Discuss the status of women in Japan.
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Discuss the differences among religious strictures, legal doctrine, and cultural practices concerning women in various societies.
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Discuss the various forms that inequality based sexual orientation takes around the world.
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Discuss the differences among religious strictures, legal doctrine, and cultural practices concerning sexual orientation in various societies.
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Discuss female genital mutilation.
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Discuss the status of women in Third World countries.
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Discuss the rape as an act of war.
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Discuss the women’s movement
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Discuss the GLBT movement


9.4: Nuclear Transmutation
Learning Objectives
- Describe the synthesis of transuranium nuclides
After the discovery of radioactivity, the field of nuclear chemistry was created and developed rapidly during the early twentieth century. A slew of new discoveries in the 1930s and 1940s, along with World War II , combined to usher in the Nuclear Age in the mid-twentieth century. Science learned how to create new substances, and certain isotopes of certain elements were found to possess the capacity to produce unprecedented amounts of energy, with the potential to cause tremendous damage during war, as well as produce enormous amounts of power for society’s needs during peace.
Synthesis of Nuclides
Nuclear transmutation is the conversion of one nuclide into another. It can occur by the radioactive decay of a nucleus, or the reaction of a nucleus with another particle. The first manmade nucleus was produced in Ernest Rutherford’s laboratory in 1919 by a transmutation reaction, the bombardment of one type of nuclei with other nuclei or with neutrons. Rutherford bombarded nitrogen atoms with high-speed α particles from a natural radioactive isotope of radium and observed protons resulting from the reaction:
\[\ce{^{14}_7N + ^4_2He ⟶ ^{17}_8O + ^1_1H} \nonumber\]
The \(\ce{^{17}_8O}\) and \(\ce{^1_1H}\) nuclei that are produced are stable, so no further (nuclear) changes occur.
To reach the kinetic energies necessary to produce transmutation reactions, devices called particle accelerators are used. These devices use magnetic and electric fields to increase the speeds of nuclear particles. In all accelerators, the particles move in a vacuum to avoid collisions with gas molecules. When neutrons are required for transmutation reactions, they are usually obtained from radioactive decay reactions or from various nuclear reactions occurring in nuclear reactors.
CERN Particle Accelerator
Located near Geneva, the CERN (“Conseil Européen pour la Recherche Nucléaire,” or European Council for Nuclear Research) Laboratory is the world’s premier center for the investigations of the fundamental particles that make up matter. It contains the 27-kilometer (17 mile) long, circular Large Hadron Collider (LHC), the largest particle accelerator in the world (Figure \(\PageIndex{1}\)). In the LHC , particles are boosted to high energies and are then made to collide with each other or with stationary targets at nearly the speed of light. Superconducting electromagnets are used to produce a strong magnetic field that guides the particles around the ring. Specialized, purpose-built detectors observe and record the results of these collisions, which are then analyzed by CERN scientists using powerful computers.
Figure \(\PageIndex{1}\): A small section of the LHC is shown with workers traveling along it. (credit: Christophe Delaere)
In 2012, CERN announced that experiments at the LHC showed the first observations of the Higgs boson, an elementary particle that helps explain the origin of mass in fundamental particles. This long-anticipated discovery made worldwide news and resulted in the awarding of the 2103 Nobel Prize in Physics to François Englert and Peter Higgs, who had predicted the existence of this particle almost 50 years previously.
Prior to 1940, the heaviest-known element was uranium, whose atomic number is 92. Now, many artificial elements have been synthesized and isolated, including several on such a large scale that they have had a profound effect on society. One of these—element 93, neptunium (Np)—was first made in 1940 by McMillan and Abelson by bombarding uranium-238 with neutrons. The reaction creates unstable uranium-239, with a half-life of 23.5 minutes, which then decays into neptunium-239. Neptunium-239 is also radioactive, with a half-life of 2.36 days, and it decays into plutonium-239. The nuclear reactions are:
\ce{^{238}_{92}U + ^1_0n} &⟶ \ce{^{239}_{92}U} && \\
\ce{^{239}_{92}U} &⟶ \ce{^{239}_{93}Np + ^0_{−1}e} &&\textrm{half-life}=\mathrm{23.5\: min} \\
\ce{^{239}_{93}Np } &⟶ \ce{^{239}_{94}Pu + ^0_{−1}e} &&\textrm{half-life}=\mathrm{2.36\: days}
\end{align*}\]
Plutonium is now mostly formed in nuclear reactors as a byproduct during the decay of uranium. Some of the neutrons that are released during U-235 decay combine with U-238 nuclei to form uranium-239; this undergoes β decay to form neptunium-239, which in turn undergoes β decay to form plutonium-239 as illustrated in the preceding three equations. It is possible to summarize these equations as:
\[\mathrm{\ce{^{238}_{92}U} + {^1_0n}⟶ \ce{^{239}_{92}U} \xrightarrow{β^-} \ce{^{239}_{93}Np} \xrightarrow{β^-} \ce{^{239}_{94}Pu}}\]
Heavier isotopes of plutonium—Pu-240, Pu-241, and Pu-242—are also produced when lighter plutonium nuclei capture neutrons. Some of this highly radioactive plutonium is used to produce military weapons, and the rest presents a serious storage problem because they have half-lives from thousands to hundreds of thousands of years.
Although they have not been prepared in the same quantity as plutonium, many other synthetic nuclei have been produced. Nuclear medicine has developed from the ability to convert atoms of one type into other types of atoms. Radioactive isotopes of several dozen elements are currently used for medical applications. The radiation produced by their decay is used to image or treat various organs or portions of the body, among other uses.
The elements beyond element 92 (uranium) are called transuranium elements . As of this writing, 22 transuranium elements have been produced and officially recognized by IUPAC; several other elements have formation claims that are waiting for approval. Some of these elements are shown in Table \(\PageIndex{1}\).
| Name | Symbol | Atomic Number | Reaction |
|---|---|---|---|
| americium | Am | 95 | \(\ce{^{239}_{94}Pu + ^1_0n ⟶ ^{240}_{95}Am + ^0_{−1}e}\) |
| curium | Cm | 96 | \(\ce{^{239}_{94}Pu + ^4_2He ⟶ ^{242}_{96}Cm + ^1_0n}\) |
| californium | Cf | 98 | \(\ce{^{242}_{96}Cm + ^4_2He⟶ ^{243}_{97}Bk + 2^1_0n}\) |
| einsteinium | Es | 99 | \(\ce{^{238}_{92}U + 15^1_0n⟶ ^{253}_{99}Es + 7^0_{−1}e}\) |
| mendelevium | Md | 101 | \(\ce{^{253}_{99}Es + ^4_2He ⟶ ^{256}_{101}Md + ^1_0n}\) |
| nobelium | No | 102 | \(\ce{^{246}_{96}Cm + ^{12}_6C ⟶ ^{254}_{102}No + 4 ^1_0n}\) |
| rutherfordium | Rf | 104 | \(\ce{^{249}_{98}Cf + ^{12}_6C⟶ ^{257}_{104}Rf + 4 ^1_0n}\) |
|
seaborgium |
Sg |
106 |
\(\ce{^{206}_{82}Pb + ^{54}_{24}Cr ⟶ ^{257}_{106}Sg + 3 ^1_0n}\) \(\ce{^{249}_{98}Cf + ^{18}_8O ⟶ ^{263}_{106}Sg + 4 ^1_0n}\) |
| meitnerium | Mt | 107 | \(\ce{^{209}_{83}Bi + ^{58}_{26}Fe ⟶ ^{266}_{109}Mt + ^1_0n}\) |
Contributors and Attributions
-
Paul Flowers (University of North Carolina - Pembroke), Klaus Theopold (University of Delaware) and Richard Langley (Stephen F. Austin State University) with contributing authors. Textbook content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at<EMAIL_ADDRESS>).


4.3: Exponential Relationships (1 of 6)
Learning Objectives
- Use an exponential model (when appropriate) to describe the relationship between two quantitative variables. Interpret the model in context.
In our first example of exponential relationships, we investigate a nonlinear model for growth in a population over time.
Example
The Return of the Bald Eagle
During the mid-20th century, the population of bald eagles in the lower 48 states declined substantially. A highly toxic pesticide, DDT, was the main cause of the decline. DDT causes damage to bird egg shells. By 1963, bald eagles were in danger of complete extinction. Only 417 pairs of bald eagles remained. In 1967, the bald eagle became an official endangered species. Then in 1972, the EPA banned the use of DDT in the United States. The impact of the ban was a dramatic turnaround in the fate of the bald eagle.
Here is the data. Note that in the table, we defined t , our explanatory variable, to be Years after 1950 . The response variable is the number of bald eagle pairs that are mating.
| Year | t = years after 1950 | Eagle Pairs |
|---|---|---|
| 1963 | 13 | 417 |
| 1974 | 24 | 791 |
| 1981 | 31 | 1188 |
| 1982 | 32 | 1480 |
| 1984 | 34 | 1757 |
| 1986 | 36 | 1875 |
| 1987 | 37 | 2238 |
| 1988 | 38 | 2475 |
| 1989 | 39 | 2680 |
| 1990 | 40 | 3035 |
| 1991 | 41 | 3399 |
| 1992 | 42 | 3749 |
| 1993 | 43 | 4015 |
| 1994 | 44 | 4449 |
| 1995 | 45 | 4712 |
| 1996 | 46 | 5094 |
| 1997 | 47 | 5295 |
| 1998 | 48 | 5748 |
| 1999 | 49 | 6104 |
| 2000 | 50 | 6471 |
Our goal is to find an equation to model this relationship.
Here is a scatterplot of the data. We can see that the relationship appears somewhat linear, particularly for years after 1980 ( t = 30). The correlation coefficient for this data set is high, r = 0.914.
The least squares regression line is Predicted eagle pairs = −3,878.11 + 185.4 t . Below is a scatterplot of the data with the least-squares regression line and the residual plot.
We see a clear pattern in the residuals, suggesting that a linear model does not capture patterns in the data.
Note: This is a reminder that a large r -value does not guarantee that a linear model is a good fit.
Conclusion: The data set for eagle pairs is clearly nonlinear. We need a better model.
In the scatterplot below, we fit an exponential model to the data. Notice how well this model describes the relationship between the variables. There is very little scatter about the exponential curve. There is a strong, positive exponential relationship between these variables.
The equation of the exponential model is Predicted eagle pairs = 121 (1.083) t .
Note: In this equation, the t -variable is an exponent. Sometimes you will see this written with the caret symbol: ^. So Predicted y = 121 (1.083) t and Predicted y = 121(1.083) ^ t mean the same thing.
Now we use the exponential model to make predictions about the number of bald eagle mating pairs. We also compare the predictions from the exponential model to the linear model. Because there is a strong exponential relationship and a weaker linear relationship in the data, we expect the predictions from the exponential model to be better.
In 1963 ( t = 13), there were 417 mating pairs.
- According to the linear model: Predicted eagle pairs = –3,878.11 + 185.4 (13) = (–1,468). Obviously, a negative value does not make sense for a count of eagle pairs.
- According to the exponential model: Predicted eagle pairs = 121 (1.083) 13 = 341. So the exponential model underestimates by 417 – 341 = 76 mating pairs. But this is a much better prediction than we got from the linear model.
In 2000 ( t = 50), there were 6,471 mating pairs.
- According to the linear model: Predicted eagle pairs = –3,878.11 + 185.4 (50) = 5,392. So the linear model underestimates by 6,471 – 5392 = 1,079 mating pairs.
- According to the exponential model: Predicted eagle pairs = 121 (1.083) 50 = 6,519. So the exponential model overestimates by 6,591 – 6,471 = 48 mating pairs. This is a much better prediction than we got from the linear model.
Contributors and Attributions
- Concepts in Statistics. Provided by : Open Learning Initiative. Located at : http://oli.cmu.edu . License : CC BY: Attribution