6.7: One Dimensional Wave Equation
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Imagine we have a tensioned guitar string of length \(L\). Suppose we only consider vibrations in one direction. That is, let \(x\) denote the position along the string, let \(t\) denote time, and let \(y\) denote the displacement of the string from the rest position. See Figure \(\PageIndex{1}\).
The equation that governs this setup is the so-called one-dimensional wave equation :
\[ y_{tt}=a^2 y_{xx}, \nonumber \]
for some constant \(a>0\). The intuition is similar to the heat equation, replacing velocity with acceleration: the acceleration at a specific point is proportional to the second derivative of the shape of the string. In other words when the string is concave down then \(u_{xx}\) is negative and the string wants to accelerate downwards, so \(u_{tt}\) should be negative. And vice versa. The wave equation is an example of a hyperbolic PDE.
Assume that the ends of the string are fixed in place:
\[y(0,t)=0 \quad\text{and}\quad y(L,t)=0. \nonumber \]
Note that we have two conditions along the \(x\) axis as there are two derivatives in the \(x\) direction.
There are also two derivatives along the \(t\) direction and hence we need two further conditions here. We need to know the initial position and the initial velocity of the string. That is, for some known functions \(f(x)\) and \(g(x)\), we impose
\[y(x,0)=f(x) \quad\text{and}\quad y_t(x,0)=g(x). \nonumber \]
As the equation is again linear, superposition works just as it did for the heat equation. And again we will use separation of variables to find enough building-block solutions to get the overall solution. There is one change however. It will be easier to solve two separate problems and add their solutions.
The two problems we will solve are
\[\label{wave:weq} \begin{array}{ll} w_{tt} = a^2 w_{xx} , & \\ w(0,t) = w(L,t) = 0 , & \\ w(x,0) = 0 & \qquad \text{for } \; 0 < x < L , \\ w_t(x,0) = g(x) & \qquad \text{for } \; 0 < x < L , \end{array} \] and \[\label{wave:zeq} \begin{array}{ll} z_{tt} = a^2 z_{xx} , & \\ z(0,t) = z(L,t) = 0 , & \\ z(x,0) = f(x) & \qquad \text{for } \; 0 < x < L , \\ z_t(x,0) = 0 & \qquad \text{for } \; 0 < x < L . \end{array} \]
The principle of superposition implies that \(y=w+z\) solves the wave equation and furthermore \( y(x,0)=w(x,0)+z(x,0)=f(x)\) and \( y_t(x,0)=w_t(x,0)+z_t(x,0)=g(x)\). Hence, \(y\) is a solution to
\[\label{wave:yeq} \begin{array}{ll} y_{tt} = a^2 y_{xx} , & \\ y(0,t) = y(L,t) = 0 , & \\ y(x,0) = f(x) & \qquad \text{for } \; 0 < x < L , \\ y_t(x,0) = g(x) & \qquad \text{for } \; 0 < x < L . \end{array} \]
The reason for all this complexity is that superposition only works for homogeneous conditions such as \(y(0,t)=y(L,t)=0\), \(y(x,0)=0\), or \(y_t(x,0)=0\). Therefore, we will be able to use the idea of separation of variables to find many building-block solutions solving all the homogeneous conditions. We can then use them to construct a solution solving the remaining nonhomogeneous condition.
Let us start with \(\eqref{wave:weq}\). We try a solution of the form \(w(x,t)=X(x)T(t)\) again. We plug into the wave equation to obtain
\[ X(x)T''(t)=a^2 X''(x)T(t). \nonumber \]
Rewriting we get
\[ \dfrac{T''(t)}{a^2 T(t)}= \dfrac{X''(x)}{X(x)}. \nonumber \]
Again, left hand side depends only on \(t\) and the right hand side depends only on \(x\). Therefore, both equal a constant, which we will denote by \(- \lambda\).
\[ \dfrac{T''(t)}{a^2 T(t)}= - \lambda = \dfrac{X''(x)}{X(x)}. \nonumber \]
We solve to get two ordinary differential equations
\[\begin{align}\begin{aligned} X''(x)+ \lambda X(x) &=0, \\ T''(t)+ \lambda a^2T(t) &=0.\end{aligned}\end{align} \nonumber \]
The conditions \(0=w(0,t)=X(0)T(t)\) implies \(X(0)=0\) and \(w(L,t)=0\) implies that \(X(L)=0\). Therefore, the only nontrivial solutions for the first equation are when \( \lambda = \lambda_n = \dfrac{n^2 \pi^2}{L^2}\) and they are
\[ X_n(x)= \sin \left( \dfrac{n \pi}{L}x \right). \nonumber \]
The general solution for \(T\) for this particular \( \lambda_n \) is
\[ T_n(t)= A \cos \left( \dfrac{n \pi a}{L}t \right) + B \sin \left( \dfrac{n \pi a}{L}t \right) . \nonumber \]
We also have the condition that \(w(x,0)=0\) or \(X(x)T(0)=0\). This implies that \(T(0)=0\), which in turn forces \(A=0\). It is convenient to pick \(B= \dfrac{L}{n \pi a}\) (you will see why in a moment) and hence
\[ T_n(t)= \dfrac{L}{n \pi a} \sin \left( \dfrac{n \pi a}{L}t \right). \nonumber \]
Our building-block solutions are
\[ w_n(x,t)= \dfrac{L}{n \pi a} \sin \left( \dfrac{n \pi }{L}x \right) \sin \left( \dfrac{n \pi a}{L}t \right). \nonumber \]
We differentiate in \(t\), that is
\[ \dfrac{\partial w_n}{\partial t}(x,t)= \sin \left( \dfrac{n \pi }{L}x \right) \cos \left( \dfrac{n \pi a}{L}t \right). \nonumber \]
Hence,
\[ \dfrac{\partial w_n}{\partial t}(x,0)= \sin \left( \dfrac{n \pi }{L}x \right) . \nonumber \]
We expand \(g(x)\) in terms of these sines as
\[ g(x)= \sum_{n=1}^{\infty} b_n \sin \left( \dfrac{n \pi}{L}x \right). \nonumber \]
Using superposition we can just write down the solution to \(\eqref{wave:weq}\) as a series
\[ w(x,t)= \sum_{n=1}^{\infty} b_n w_n(x,t) = \sum_{n=1}^{\infty} b_n \dfrac{L}{n \pi a} \sin \left( \dfrac{n \pi }{L}x \right) \sin \left( \dfrac{n \pi a}{L}t \right). \nonumber \]
Exercise \(\PageIndex{1}\)
Check that \(w(x,0)=0\) and \(w_t(x,0)=g(x)\).
Similarly we proceed to solve \(\eqref{wave:zeq}\). We again try \(z(x,y)=X(x)T(t)\). The procedure works exactly the same at first. We obtain
\[\begin{align}\begin{aligned} X''(x)+ \lambda X(x) &=0, \\ T''(t)+ \lambda a^2T(t) &=0.\end{aligned}\end{align} \nonumber \]
and the conditions \(X(0)=0\), \(X(L)=0\). So again \( \lambda = \lambda_n = \dfrac{n^2 \pi^2}{L^2}\) and
\[ X_n(x)= \sin \left( \dfrac{n \pi}{L}x \right). \nonumber \]
This time the condition on \(T\) is \(T'(0)=0\). Thus we get that \(B=0\) and we take
\[ T_n(t)= \cos \left( \dfrac{n \pi a}{L}t \right). \nonumber \]
Our building-block solution will be
\[ z_n(x,t)= \sin \left( \dfrac{n \pi}{L}x \right) \cos \left( \dfrac{n \pi a}{L}t \right). \nonumber \]
As \(z_{n}(x,0)=\sin\left(\frac{n\pi}{L}x\right)\), we expand \(f(x)\) in terms of these sines as
\[ f(x)= \sum_{n=1}^{\infty}c_n \sin \left( \dfrac{n \pi}{L}x \right). \nonumber \]
And we write down the solution to \(\eqref{wave:zeq}\) as a series
\[ z(x,t)= \sum_{n=1}^{\infty}c_n z_n (x,t)= \sum_{n=1}^{\infty} c_n \sin \left( \dfrac{n \pi}{L}x \right) \cos \left( \dfrac{n \pi a}{L}t \right). \nonumber \]
Exercise \(\PageIndex{2}\)
Fill in the details in the derivation of the solution of \(\eqref{wave:zeq}\). Check that the solution satisfies all the side conditions.
Putting these two solutions together, let us state the result as a theorem.
Theorem \(\PageIndex{1}\)
Take the equation
\[\label{wave:tyeq} \begin{array}{ll} y_{tt} = a^2 y_{xx} , & \\ y(0,t) = y(L,t) = 0 , & \\ y(x,0) = f(x) & \qquad \text{for } \; 0 < x < L , \\ y_t(x,0) = g(x) & \qquad \text{for } \; 0 < x < L , \end{array} \]
where
\[ f(x)= \sum_{n=1}^{\infty} c_n \sin \left( \dfrac{n \pi}{L}x \right), \nonumber \]
and
\[ g(x)= \sum_{n=1}^{\infty} b_n \sin \left( \dfrac{n \pi}{L}x \right). \nonumber \]
Then the solution \( y(x,t)\) can be written as a sum of the solutions of (4.7.4) and (4.7.5). In other words,
\[\begin{align}\begin{aligned} y(x,t) &= \sum_{n=1}^{\infty} b_n \dfrac{L}{n \pi a} \sin \left( \dfrac{n \pi}{L}x \right) \sin \left( \dfrac{n \pi a}{L}t \right) + c_n \sin \left( \dfrac{n \pi}{L}x \right) \cos \left( \dfrac{n \pi a}{L}t \right) \\ &= \sum_{n=1}^{\infty} \sin \left( \dfrac{n \pi}{L}x \right) \left[ b_n \dfrac{L}{n \pi a} \sin \left( \dfrac{n \pi a}{L}t \right) +c_n \cos \left( \dfrac{n \pi a}{L}t \right) \right].\end{aligned}\end{align} \nonumber \]
Example \(\PageIndex{1}\)
Let us try a simple example of a plucked string. Suppose that a string of length 2 is plucked in the middle such that it has the initial shape given in Figure \(\PageIndex{2}\). That is
\[ f(x)= \left\{ \begin{array}{cc} 0.1x & {\rm{if}}~ 0 \leq x \leq 1, \\ 0.1(2-x) & {\rm{if}}~ 1 < x \leq 2 \end{array} \right. . \nonumber \]
The string starts at rest (\(g(x)=0\)). Suppose that \(a=1\) in the wave equation for simplicity. In other words, we wish to solve the problem:
\[\begin{align}\begin{aligned} & y_{tt} = y_{xx}, \\ & y(0,t) = y(2,t)= 0 , \\ & y(x,0) = f(x) \quad \text{and} \quad y_t(x,0)= 0 .\end{aligned}\end{align} \nonumber \]
We leave it to the reader to compute the sine series of \(f(x)\). The series will be
\[f(x)= \sum_{n=1}^{\infty} \dfrac{0.8}{n^2 \pi^2} \sin \left( \dfrac{n \pi}{2} \right) \sin \left( \dfrac{n \pi}{2} x \right). \nonumber \]
Note that \( \sin \left( \dfrac{n \pi}{2} \right) \) is the sequence \(1,0,-1,0,1,0,-1, \ldots\) for \(n=1,2,3,4, \ldots\). Therefore,
\[ f(x)= \dfrac{0.8}{ \pi^2} \sin \left( \dfrac{\pi}{2}x \right) - \dfrac{0.8}{9 \pi^2} \sin \left( \dfrac{3 \pi}{2}x \right) + \dfrac{0.8}{25 \pi^2} \sin \left( \dfrac{5 \pi}{2}x \right) - \cdots \nonumber \]
The solution \(y(x,t)\) is given by
\[\begin{align}\begin{aligned} y(x,t) & = \sum_{n=1}^\infty \frac{0.8}{n^2 \pi^2} \sin \left( \frac{n \pi}{2} \right) \sin \left( \frac{n \pi}{2} x \right) \cos \left( \frac{n \pi}{2} t \right) \\ & = \sum_{m=1}^\infty \frac{0.8 {(-1)}^{m+1}}{{(2m-1)}^2 \pi^2} \sin \left( \frac{(2m-1) \pi}{2} x \right) \cos \left( \frac{(2m-1) \pi}{2} t \right) \\ & = \frac{0.8}{\pi^2} \sin \left( \frac{\pi}{2} x \right) \cos \left( \frac{\pi}{2} t \right) - \frac{0.8}{9 \pi^2} \sin \left( \frac{3 \pi}{2} x \right) \cos \left( \frac{3 \pi}{2} t \right) \\ & \hspace{20em} + \frac{0.8}{25 \pi^2} \sin \left( \frac{5 \pi}{2} x \right) \cos \left( \frac{5 \pi}{2} t \right) - \cdots \end{aligned}\end{align} \nonumber \]
See Figure \(\PageIndex{3}\) for a plot for \(0 < t < 3\). Notice that unlike the heat equation, the solution does not become "smoother," the "sharp edges" remain. We will see the reason for this behavior in the next section where we derive the solution to the wave equation in a different way.
Make sure you understand what the plot, such as the one in the figure, is telling you. For each fixed \(t\), you can think of the function \(y(x,t)\) as just a function of \(x\). This function gives you the shape of the string at time \(t\). See Figure \(\PageIndex{4}\) for plots of at \(y\) as a function of \(x\) at several different values of \(t\). On this plot you can see the sharp edges remaining much better.
One thing to take away from all this is how a guitar sounds. Notice that the (angular) frequencies that come up in the solution are \(n \frac{\pi a}{L}\). That is, there is a certain base fundamental frequency \(\frac{\pi a}{L}\), and then we also get all the multiples of this frequency, which in music are called the overtones . Which overtones appear and with what amplitude is what musicians call the timbre of the note. Mathematicians usually call this the spectrum . Because all the frequencies are multiples of one frequency (the fundamental) we get a nice pleasing sound.
The fundamental frequency \(\frac{\pi a}{L}\) increases as we decrease length \(L\).  The constant \(a\) is given by \[a = \sqrt{\frac{T}{\rho}} , \nonumber \] where \(T\) is tension and \(\rho\) is the linear density of the string. Tightening the string (turning the tuning peg on a guitar) increases \(a\) and hence produces a higher fundamental frequency (a higher note). On the other hand using a heavier string reduces \(a\) and produces a lower fundamental frequency (a lower note). A bass guitar has longer thicker strings, while a ukulele has short strings made of lighter material.
Something rather interesting is the almost symmetry between space and time. In its simplest form we see this symmetry in the solutions \[\sin \left( \frac{n \pi}{L} x \right) \sin \left( \frac{n \pi a}{L} t \right) . \nonumber \] Except for the \(a\), time and space are just the same.
In general, the solution for a fixed \(x\) is a Fourier series in \(t\), for a fixed \(t\) it is a Fourier series in \(x\), and the coefficients are related. If the shape \(f(x)\) or the initial velocity have lots of corners, then the sound wave will have lots of corners. That is because the Fourier coefficients of the initial shape decay to zero (as \(n \to \infty\)) at the same rate as the Fourier coefficients of the wave in time (for some fixed \(x\)). So if you use a sharp object to pick the string, you get a sharper sound with lots of high frequency components, while if you use your thumb, you get a softer sound without so many high overtones. Similarly if you pluck close to the bridge, you are getting a pluck that looks more like the sawtooth, and you get an even sharper sound.
In fact, if you look at the formula for the solution, you see that for any fixed \(x\) we get an almost arbitrary Fourier series in \(t\), everything except the constant term. You can essentially obtain any sound you want by plucking the string in just the right way. Of course we are considering an ideal string of no stiffness and no air resistance. Those variables clearly impact the sound as well.


8.20: Contribution Margin Ratio
Learning Outcomes
- Compute the contribution margin ratio
It is Thursday morning and your boss just called you into her office. “Why is our net profit down 10% this quarter? It looks like our cost of goods sold has gone up dramatically! Can you check into this and get back to me before the end of the day?” You need to put on your thinking cap and figure out why net profit has dipped. She mentioned that our cost of goods sold was higher. Could there have been a price increase on one of the components of our product? Off to visit purchasing to do some research!
The contribution margin ratio is the difference between a company’s sales and variable costs, expressed as a percentage. This ratio shows the amount of money available to cover fixed costs. It is good to have a high contribution margin ratio, as the higher the ratio, the more money per product sold is available to cover all the other expenses.
Contribution margin ratio formula:
\(\displaystyle\frac{\text{sales}-\text{variable expenses}}{\text{sales}}\)
If we go back to our Monte Corporation example, we can calculate their contribution margin ratio as follows:
\(\text{sales}=\$2000\), and \(\text{variable expenses}=\$800\), so
\(\displaystyle\frac{\$2000-\$800}{\$2000}=60\%\)
For every additional widget sold, 60% of the selling price is available for use to pay fixed costs.
What would happen if a supplier raised their price by $1 per unit on a part for the widget? This would increase the variable costs by $1 per unit, bringing the variable cost per unit to $5. How would this affect the contribution margin ratio for Monte Corporation?
\(\text{sales}=\$2000\), and \(\text{variable expenses}=\$1000\), so
\(\displaystyle\frac{\$2000-\$1000}{\$2000}=50\%\)
The addition of $1 per item of variable cost lowered the contribution margin ratio by a whopping 10%. You can see how much costs can affect profits for a company, and why it is important to keep costs low.
As a manager, you may be asked to negotiate or talk with vendors and perhaps even to ask for discounts. Small differences in prices of your supplies can make a huge difference in the profitability of a company.
Practice Questions


6.1: Prokaryote Habitats, Relationships, and Microbiomes
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- Ying Liu
- City College of San Francisco
Learning Objectives
- Identify and describe unique examples of prokaryotes in various habitats on earth
- Identify and describe symbiotic relationships
- Compare normal/commensal/resident microbiota to transient microbiota
- Explain how prokaryotes are classified
Clinical Focus: Part 1
Marsha, a 20-year-old university student, recently returned to the United States from a trip to Nigeria, where she had interned as a medical assistant for an organization working to improve access to laboratory services for tuberculosis testing. When she returned, Marsha began to feel fatigue, which she initially attributed to jet lag. However, the fatigue persisted, and Marsha soon began to experience other bothersome symptoms, such as occasional coughing, night sweats, loss of appetite, and a low-grade fever of 37.4 °C (99.3 °F).
Marsha expected her symptoms would subside in a few days, but instead, they gradually became more severe. About two weeks after returning home, she coughed up some sputum and noticed that it contained blood and small whitish clumps resembling cottage cheese. Her fever spiked to 38.2 °C (100.8 °F), and she began feeling sharp pains in her chest when breathing deeply. Concerned that she seemed to be getting worse, Marsha scheduled an appointment with her physician.
Exercise \(\PageIndex{1}\)
Could Marsha’s symptoms be related to her overseas travel, even several weeks after returning home?
All living organisms are classified into three domains of life: Archaea, Bacteria, and Eukarya. In this chapter, we will focus on the domains Archaea and Bacteria. Archaea and bacteria are unicellular prokaryotic organisms. Unlike eukaryotes, they have no nuclei or any other membrane-bound organelles.
Prokaryote Habitats and Functions
Prokaryotes are ubiquitous. They can be found everywhere on our planet, even in hot springs, in the Antarctic ice shield, and under extreme pressure two miles under water. One bacterium, Paracoccus denitrificans , has even been shown to survive when scientists removed it from its native environment (soil) and used a centrifuge to subject it to forces of gravity as strong as those found on the surface of Jupiter.
Prokaryotes also are abundant on and within the human body. According to a report by National Institutes of Health, prokaryotes, especially bacteria, outnumber human cells 10:1. 1 More recent studies suggest the ratio could be closer to 1:1, but even that ratio means that there are a great number of bacteria within the human body. 2 Bacteria thrive in the human mouth, nasal cavity, throat, ears, gastrointestinal tract, and vagina. Large colonies of bacteria can be found on healthy human skin, especially in moist areas (armpits, navel, and areas behind ears). However, even drier areas of the skin are not free from bacteria.
The existence of prokaryotes is very important for the stability and thriving of ecosystems. For example, they are a necessary part of soil formation and stabilization processes through the breakdown of organic matter and development of biofilms. One gram of soil contains up to 10 billion microorganisms (most of them prokaryotic) belonging to about 1,000 species. Many species of bacteria use substances released from plant roots, such as acids and carbohydrates, as nutrients. The bacteria metabolize these plant substances and release the products of bacterial metabolism back to the soil, forming humus and thus increasing the soil’s fertility. In salty lakes such as the Dead Sea (Figure \(\PageIndex{1}\)), salt-loving halobacteria decompose dead brine shrimp and nourish young brine shrimp and flies with the products of bacterial metabolism.
In addition to living in the ground and the water, prokaryotic microorganisms are abundant in the air, even high in the atmosphere. There may be up to 2,000 different kinds of bacteria in the air, similar to their diversity in the soil.
Prokaryotes can be found everywhere on earth because they are extremely resilient and adaptable. They are often metabolically flexible, which means that they might easily switch from one energy source to another, depending on the availability of the sources, or from one metabolic pathway to another. For example, certain prokaryotic cyanobacteria can switch from a conventional type of lipid metabolism, which includes production of fatty aldehydes, to a different type of lipid metabolism that generates biofuel, such as fatty acids and wax esters. Groundwater bacteria store complex high-energy carbohydrates when grown in pure groundwater, but they metabolize these molecules when the groundwater is enriched with phosphates. Some bacteria get their energy by reducing sulfates into sulfides, but can switch to a different metabolic pathway when necessary, producing acids and free hydrogen ions.
Prokaryotes perform functions vital to life on earth by capturing (or “fixing”) and recycling elements like carbon and nitrogen. Organisms such as animals require organic carbon to grow, but, unlike prokaryotes, they are unable to use inorganic carbon sources like carbon dioxide. Thus, animals rely on prokaryotes to convert carbon dioxide into organic carbon products that they can use. This process of converting carbon dioxide to organic carbon products is called carbon fixation.
Plants and animals also rely heavily on prokaryotes for nitrogen fixation, the conversion of atmospheric nitrogen into ammonia, a compound that some plants can use to form many different biomolecules necessary to their survival. Bacteria in the genus Rhizobium , for example, are nitrogen-fixing bacteria; they live in the roots of legume plants such as clover, alfalfa, and peas (Figure \(\PageIndex{2}\)). Ammonia produced by Rhizobium helps these plants to survive by enabling them to make building blocks of nucleic acids. In turn, these plants may be eaten by animals—sustaining their growth and survival—or they may die, in which case the products of nitrogen fixation will enrich the soil and be used by other plants.
Another positive function of prokaryotes is in cleaning up the environment. Recently, some researchers focused on the diversity and functions of prokaryotes in manmade environments. They found that some bacteria play a unique role in degrading toxic chemicals that pollute water and soil. 3
Despite all of the positive and helpful roles prokaryotes play, some are human pathogens that may cause illness or infection when they enter the body. In addition, some bacteria can contaminate food, causing spoilage or foodborne illness, which makes them subjects of concern in food preparation and safety. Less than 1% of prokaryotes (all of them bacteria) are thought to be human pathogens, but collectively these species are responsible for a large number of the diseases that afflict humans.
Besides pathogens, which have a direct impact on human health, prokaryotes also affect humans in many indirect ways. For example, prokaryotes are now thought to be key players in the processes of climate change. In recent years, as temperatures in the earth’s polar regions have risen, soil that was formerly frozen year-round (permafrost) has begun to thaw. Carbon trapped in the permafrost is gradually released and metabolized by prokaryotes. This produces massive amounts of carbon dioxide and methane, greenhouse gases that escape into the atmosphere and contribute to the greenhouse effect.
Exercise \(\PageIndex{2}\)
- In what types of environments can prokaryotes be found?
- Name some ways that plants and animals rely on prokaryotes.
Symbiotic Relationships
As we have learned, prokaryotic microorganisms can associate with plants and animals. Often, this association results in unique relationships between organisms. For example, bacteria living on the roots or leaves of a plant get nutrients from the plant and, in return, produce substances that protect the plant from pathogens. On the other hand, some bacteria are plant pathogens that use mechanisms of infection similar to bacterial pathogens of animals and humans.
Prokaryotes live in a community, or a group of interacting populations of organisms. A population is a group of individual organisms belonging to the same biological species and limited to a certain geographic area. Populations can have cooperative interactions, which benefit the populations, or competitive interactions, in which one population competes with another for resources. The study of these interactions between populations is called microbial ecology.
Any interaction between different species within a community is called symbiosis. Such interactions fall along a continuum between opposition and cooperation. Interactions in a symbiotic relationship may be beneficial or harmful, or have no effect on one or both of the species involved. Table \(\PageIndex{1}\) summarizes the main types of symbiotic interactions among prokaryotes.
| Type | Population A | Population B |
|---|---|---|
| Mutualism | Benefitted | Benefitted |
| Amensalism | Harmed | Unaffected |
| Commensalism | Benefitted | Unaffected |
| Neutralism | Unaffected | Unaffected |
| Parasitism | Benefitted | Harmed |
When two species benefit from each other, the symbiosis is called mutualism (or syntropy, or crossfeeding). For example, humans have a mutualistic relationship with the bacterium Bacteroides thetaiotetraiotamicron , which lives in the intestinal tract. B. thetaiotetraiotamicron digests complex polysaccharide plant materials that human digestive enzymes cannot break down, converting them into monosaccharides that can be absorbed by human cells. Humans also have a mutualistic relationship with certain strains of Escherichia coli , another bacterium found in the gut. E. coli relies on intestinal contents for nutrients, and humans derive certain vitamins from E. coli, particularly vitamin K, which is required for the formation of blood clotting factors. (This is only true for some strains of E. coli , however. Other strains are pathogenic and do not have a mutualistic relationship with humans.)
A type of symbiosis in which one population harms another but remains unaffected itself is called amensalism. In the case of bacteria, some amensalist species produce bactericidal substances that kill other species of bacteria. For example, the bacterium Lucilia sericata produces a protein that destroys Staphylococcus aureus , a bacterium commonly found on the surface of the human skin. Too much handwashing can affect this relationship and lead to S. aureus diseases and transmission.
In another type of symbiosis, called commensalism, one organism benefits while the other is unaffected. This occurs when the bacterium Staphylococcus epidermidis uses the dead cells of the human skin as nutrients. Billions of these bacteria live on our skin, but in most cases (especially when our immune system is healthy), we do not react to them in any way.
If neither of the symbiotic organisms is affected in any way, we call this type of symbiosis neutralism. An example of neutralism is the coexistence of metabolically active (vegetating) bacteria and endospores (dormant, metabolically passive bacteria). For example, the bacterium Bacillus anthracis typically forms endospores in soil when conditions are unfavorable. If the soil is warmed and enriched with nutrients, some endospores germinate and remain in symbiosis with other endospores that have not germinated.
A type of symbiosis in which one organism benefits while harming the other is called parasitism. The relationship between humans and many pathogenic prokaryotes can be characterized as parasitic because these organisms invade the body, producing toxic substances or infectious diseases that cause harm. Diseases such as tetanus, diphtheria, pertussis, tuberculosis, and leprosy all arise from interactions between bacteria and humans.
Scientists have coined the term microbiome to refer to all prokaryotic and eukaryotic microorganisms that are associated with a certain organism. Within the human microbiome, there are resident microbiota and transient microbiota. The resident microbiota consists of microorganisms that constantly live in or on our bodies. The term transient microbiota refers to microorganisms that are only temporarily found in the human body, and these may include pathogenic microorganisms. Hygiene and diet can alter both the resident and transient microbiota.
The resident microbiota is amazingly diverse, not only in terms of the variety of species but also in terms of the preference of different microorganisms for different areas of the human body. For example, in the human mouth, there are thousands of commensal or mutualistic species of bacteria. Some of these bacteria prefer to inhabit the surface of the tongue, whereas others prefer the internal surface of the cheeks, and yet others prefer the front or back teeth or gums. The inner surface of the cheek has the least diverse microbiota because of its exposure to oxygen. By contrast, the crypts of the tongue and the spaces between teeth are two sites with limited oxygen exposure, so these sites have more diverse microbiota, including bacteria living in the absence of oxygen (e.g., Bacteroides , Fusobacterium ). Differences in the oral microbiota between randomly chosen human individuals are also significant. Studies have shown, for example, that the prevalence of such bacteria as Streptococcus , Haemophilus , Neisseria , and others was dramatically different when compared between individuals. 4
There are also significant differences between the microbiota of different sites of the same human body. The inner surface of the cheek has a predominance of Streptococcus , whereas in the throat, the palatine tonsil, and saliva, there are two to three times fewer Streptococcus , and several times more Fusobacterium . In the plaque removed from gums, the predominant bacteria belong to the genus Fusobacterium. However, in the intestine, both Streptococcus and Fusobacterium disappear, and the genus Bacteroides becomes predominant.
Not only can the microbiota vary from one body site to another, the microbiome can also change over time within the same individual. Humans acquire their first inoculations of normal flora during natural birth and shortly after birth. Before birth, there is a rapid increase in the population of Lactobacillus spp. in the vagina, and this population serves as the first colonization of microbiota during natural birth. After birth, additional microbes are acquired from health-care providers, parents, other relatives, and individuals who come in contact with the baby. This process establishes a microbiome that will continue to evolve over the course of the individual’s life as new microbes colonize and are eliminated from the body. For example, it is estimated that within a 9-hour period, the microbiota of the small intestine can change so that half of the microbial inhabitants will be different. 5 The importance of the initial Lactobacillus colonization during vaginal child birth is highlighted by studies demonstrating a higher incidence of diseases in individuals born by cesarean section, compared to those born vaginally. Studies have shown that babies born vaginally are predominantly colonized by vaginal lactobacillus, whereas babies born by cesarean section are more frequently colonized by microbes of the normal skin microbiota, including common hospital-acquired pathogens.
Throughout the body, resident microbiotas are important for human health because they occupy niches that might be otherwise taken by pathogenic microorganisms. For instance, Lactobacillus spp. are the dominant bacterial species of the normal vaginal microbiota for most women. lactobacillus produce lactic acid, contributing to the acidity of the vagina and inhibiting the growth of pathogenic yeasts. However, when the population of the resident microbiota is decreased for some reason (e.g., because of taking antibiotics), the pH of the vagina increases, making it a more favorable environment for the growth of yeasts such as Candida albicans . Antibiotic therapy can also disrupt the microbiota of the intestinal tract and respiratory tract, increasing the risk for secondary infections and/or promoting the long-term carriage and shedding of pathogens.
Exercise \(\PageIndex{3}\)
- Explain the difference between cooperative and competitive interactions in microbial communities.
- List the types of symbiosis and explain how each population is affected.
Taxonomy and Systematics
Assigning prokaryotes to a certain species is challenging. They do not reproduce sexually, so it is not possible to classify them according to the presence or absence of interbreeding. Also, they do not have many morphological features. Traditionally, the classification of prokaryotes was based on their shape, staining patterns, and biochemical or physiological differences. More recently, as technology has improved, the nucleotide sequences in genes have become an important criterion of microbial classification.
In 1923, American microbiologist David Hendricks Bergey (1860–1937) published A Manual in Determinative Bacteriology. With this manual, he attempted to summarize the information about the kinds of bacteria known at that time, using Latin binomial classification. Bergey also included the morphological, physiological, and biochemical properties of these organisms. His manual has been updated multiple times to include newer bacteria and their properties. It is a great aid in bacterial taxonomy and methods of characterization of bacteria. A more recent sister publication, the five-volume Bergey’s Manual of Systematic Bacteriology , expands on Bergey’s original manual. It includes a large number of additional species, along with up-to-date descriptions of the taxonomy and biological properties of all named prokaryotic taxa. This publication incorporates the approved names of bacteria as determined by the List of Prokaryotic Names with Standing in Nomenclature (LPSN).
Classification by Staining Patterns
According to their staining patterns, which depend on the properties of their cell walls, bacteria have traditionally been classified into gram-positive, gram-negative, and “atypical,” meaning neither gram-positive nor gram-negative. As explained in Staining Microscopic Specimens , gram-positive bacteria possess a thick peptidoglycan cell wall that retains the primary stain (crystal violet) during the decolorizing step; they remain purple after the gram-stain procedure because the crystal violet dominates the light red/pink color of the secondary counterstain, safranin. In contrast, gram-negative bacteria possess a thin peptidoglycan cell wall that does not prevent the crystal violet from washing away during the decolorizing step; therefore, they appear light red/pink after staining with the safranin. Bacteria that cannot be stained by the standard Gram stain procedure are called atypical bacteria. Included in the atypical category are species of Mycoplasma and Chlamydia , which lack a cell wall and therefore cannot retain the gram-stain reagents. Rickettsia are also considered atypical because they are too small to be evaluated by the Gram stain.
More recently, scientists have begun to further classify gram-negative and gram-positive bacteria. They have added a special group of deeply branching bacteria based on a combination of physiological, biochemical, and genetic features. They also now further classify gram-negative bacteria into Proteobacteria, Cytophaga-Flavobacterium-Bacteroides (CFB), and spirochetes.
The deeply branching bacteria are thought to be a very early evolutionary form of bacteria (see Deeply Branching Bacteria ). They live in hot, acidic, ultraviolet-light-exposed, and anaerobic (deprived of oxygen) conditions. Proteobacteria is a phylum of very diverse groups of gram-negative bacteria; it includes some important human pathogens (e.g., E. coli and Bordetella pertussis ). The CFB group of bacteria includes components of the normal human gut microbiota, like Bacteroides . The spirochetes are spiral-shaped bacteria and include the pathogen Treponema pallidum , which causes syphilis. We will characterize these groups of bacteria in more detail later in the chapter.
Based on their prevalence of guanine and cytosine nucleotides, gram-positive bacteria are also classified into low G+C and high G+C gram-positive bacteria. The low G+C gram-positive bacteria have less than 50% of guanine and cytosine nucleotides in their DNA. They include human pathogens, such as those that cause anthrax ( Bacillus anthracis ), tetanus ( Clostridium tetani ), and listeriosis ( Listeria monocytogenes ). High G+C gram-positive bacteria, which have more than 50% guanine and cytosine nucleotides in their DNA, include the bacteria that cause diphtheria ( Corynebacterium diphtheriae ), tuberculosis ( Mycobacterium tuberculosis ), and other diseases.
The classifications of prokaryotes are constantly changing as new species are being discovered. We will describe them in more detail, along with the diseases they cause, in later sections and chapters.
Exercise \(\PageIndex{4}\)
How do scientists classify prokaryotes?
Human Microbiome Project
The Human Microbiome Project was launched by the National Institutes of Health (NIH) in 2008. One main goal of the project is to create a large repository of the gene sequences of important microbes found in humans, helping biologists and clinicians understand the dynamics of the human microbiome and the relationship between the human microbiota and diseases. A network of labs working together has been compiling the data from swabs of several areas of the skin, gut, and mouth from hundreds of individuals.
One of the challenges in understanding the human microbiome has been the difficulty of culturing many of the microbes that inhabit the human body. It has been estimated that we are only able to culture 1% of the bacteria in nature and that we are unable to grow the remaining 99%. To address this challenge, researchers have used metagenomic analysis, which studies genetic material harvested directly from microbial communities, as opposed to that of individual species grown in a culture. This allows researchers to study the genetic material of all microbes in the microbiome, rather than just those that can be cultured. 6
One important achievement of the Human Microbiome Project is establishing the first reference database on microorganisms living in and on the human body. Many of the microbes in the microbiome are beneficial, but some are not. It was found, somewhat unexpectedly, that all of us have some serious microbial pathogens in our microbiota. For example, the conjunctiva of the human eye contains 24 genera of bacteria and numerous pathogenic species. 7 A healthy human mouth contains a number of species of the genus Streptococcus , including pathogenic species S. pyogenes and S. pneumoniae . 8 This raises the question of why certain prokaryotic organisms exist commensally in certain individuals but act as deadly pathogens in others. Also unexpected was the number of organisms that had never been cultured. For example, in one metagenomic study of the human gut microbiota, 174 new species of bacteria were identified. 9
Another goal for the near future is to characterize the human microbiota in patients with different diseases and to find out whether there are any relationships between the contents of an individual’s microbiota and risk for or susceptibility to specific diseases. Analyzing the microbiome in a person with a specific disease may reveal new ways to fight diseases.
Summary
- Prokaryotes are unicellular microorganisms whose cells have no nucleus.
- Prokaryotes can be found everywhere on our planet, even in the most extreme environments.
- Prokaryotes are very flexible metabolically, so they are able to adjust their feeding to the available natural resources.
- Prokaryotes live in communities that interact among themselves and with large organisms that they use as hosts (including humans).
- The totality of forms of prokaryotes (particularly bacteria) living on the human body is called the human microbiome, which varies between regions of the body and individuals, and changes over time.
- The totality of forms of prokaryotes (particularly bacteria) living in a certain region of the human body (e.g., mouth, throat, gut, eye, vagina) is called the microbiota of this region.
- Prokaryotes are classified into domains Archaea and Bacteria.
- In recent years, the traditional approaches to classification of prokaryotes have been supplemented by approaches based on molecular genetics.
Footnotes
- 1 Medical Press. “Mouth Bacteria Can Change Their Diet, Supercomputers Reveal.” August 12, 2014. medicalxpress.com/news/2014-0...rs-reveal.html. Accessed February 24, 2015.
- 2 A. Abbott. “Scientists Bust Myth That Our Bodies Have More Bacteria Than Human Cells: Decades-Old Assumption about Microbiota Revisited.” Nature. http://www.nature.com/news/scientist...-cells-1.19136 . Accessed June 3, 2016.
- 3 A.M. Kravetz “Unique Bacteria Fights Man-Made Chemical Waste.” 2012. www.livescience.com/25181-bac...s-nsf-bts.html. Accessed March 9, 2015.
- 4 E.M. Bik et al. “Bacterial Diversity in the Oral Cavity of 10 Healthy Individuals.” The ISME Journal 4 no. 8 (2010):962–974.
- 5 C.C. Booijink et al. “High Temporal and Intra-Individual Variation Detected in the Human Ileal Microbiota.” Environmental Microbiology 12 no. 12 (2010):3213–3227.
- 6 National Institutes of Health. “Human Microbiome Project. Overview.” commonfund.nih.gov/hmp/overview. Accessed June 7, 2016.
- 7 Q. Dong et al. “Diversity of Bacteria at Healthy Human Conjunctiva.” Investigative Ophthalmology & Visual Science 52 no. 8 (2011):5408–5413.
- 8 F.E. Dewhirst et al. “The Human Oral Microbiome.” Journal of Bacteriology 192 no. 19 (2010):5002–5017.
- 9 J.C. Lagier et al. “Microbial Culturomics: Paradigm Shift in the Human Gut Microbiome Study.” Clinical Microbiology and Infection 18 no. 12 (2012):1185–1193.


1.2: Building Your Molecules - Energy Optimization
Before we proceed into building molecules, I would like to first briefly introduce Energy Optimization or sometimes known as Energy Minimization . Avogadro finds the most stable form, lowest energy, of the molecule by minimizing all the interactions within the molecule. It does so by using advanced algorithms by applying a force field.
1) We are going to begin building Methane (CH 4 ). Click the pen, or draw tool , on the tool ribbon as shown in Figure \(\PageIndex{1}\) below.
2) The display types window and tool settings window should be on your screen. If not, simply click on the tool settings and display settings next to the tool ribbon. From the draw settings window, you are able to select the elements you wish to draw with. There is also an adjust hydrogens checkbox. This adds hydrogens to the atom based off the valency of the atom in order to fulfill the octet rule. For example, click on element drop box in the draw settings window and select carbon, see figure II. On the black screen, click on the spot you wish to put the atom. The carbon comes up with four hydrogen atoms (CH 4 ), see figure II. If you do this with oxygen, the atom will appear with two hydrogens (try some other atoms on your own and see the octet rule in action).
Note : The actually setting that would be found in the tool setting window depends on which tool you have selected and are working with.
3) CH 4 (methane) has a tetrahedral geometry. The angle and bond distances are as follows:
where the distance is given in picometers. Please note Avogadro gives the distance in angstroms. To check the angles, go to angle properties (see step 5 in Section 1). To check the lengths, go to bond properties (see step 5 in Section 1). Because methane is a simple molecule, and if you have the adjust hydrogen checked off, then Avogadro usually gives the correct geometry. See below, figure IV, for the bond and angle properties of the methane drawn in Figure \(\PageIndex{2}\). Geometry is important in energy optimization.
4) For the purpose of understanding energy optimization, let’s draw methane without the adjust hydrogens . To do so, click the draw tool , select carbon from the element list, and place anywhere on the black screen. Then select hydrogen. In order to make the bond between atoms, you must CLICK AND HOLD on the starting atom (carbon), and then DRAG from the clicked atom (carbon) over to the position in which you want the other atom (hydrogen) to be. See figure VI for the drawn molecule.
NOTE: If you wish to make a single bond to a double bond, click on the bond once. To make it a triple bond, click on it once more.
The length and angles are not in the correct geometry. To fix this, we are going to use the auto optimization tool , Figure \(\PageIndex{6}\). Avogadro applies a force field (using some very fancy algorithms of course), to obtain the optimized structure. Working with larger and more complex structures could sometimes lead to using different optimization options. But, for now we will use the settings shown in Figure \(\PageIndex{6}\) for the simple and small molecules we are working with. Click on Start . You Stop the optimization once the change in energy (dE) is equal to zero or about zero, Figure \(\PageIndex{6}\). The E is equal to the lowest energy value. Check the properties. You should now have the correct geometry.
5) Now let’s do Ammonia (NH 3 ). Ammonia has a trigonal geometry. The lone pair of electrons repel the hydrogen atoms making an angle of 107°. Draw ammonia with the adjusted hydrogens. Check the bond angles. If the bond angles do not equal 107°, then optimize the structure. Sometimes, you may not get the exact bond angle using the auto optimization tool . This is usually not a problem if the angle is almost or about the desired angle. However, you could also get a better geometry through one more step. Go to the toolbar under Extension > Optimize Geometry . Check to see if you now have an angle closer to the one you desire. See Figure \(\PageIndex{7}\) for drawn ammonia and the angle properties.
6) Now, we will look at an optimized iodomethane (CH 3 I). See Figure \(\PageIndex{8}\). Try optimizing the structure on your own!
Try drawing this structure for fun and practice!
The benzene ring (C 6 H 6) is very important organic compound and is classed as an aromatic hydrocarbon. Fun fact: the word “aromatic” comes from the fact that these compounds usually produces a sweet aroma


10.1: Prelude to The Nature of Light
Our investigation of light revolves around two questions of fundamental importance:
- What is the nature of light, and
- how does light behave under various circumstances?
Answers to these questions can be found in Maxwell’s equations , which predict the existence of electromagnetic waves and their behavior. Examples of light include radio and infrared waves, visible light, ultraviolet radiation, and X-rays. Interestingly, not all light phenomena can be explained by Maxwell’s theory. Experiments performed early in the twentieth century showed that light has corpuscular, or particle-like, properties. The idea that light can display both wave and particle characteristics is called wave-particle duality, which is examined in Photons and Matter Waves.
In this chapter, we study the basic properties of light. In the next few chapters, we investigate the behavior of light when it interacts with optical devices such as mirrors, lenses, and apertures.


4.8: Graphing Functions (without using Calculus)
There are some basic functions, called toolkit functions, that students should recognize by their function definition and their graph. For each of these functions, \(x\) is the input variable, and \(f(x)\) is the output variable. The following graphics are from the OER textbook Business Calculus by Calaway, Hoffman and Lippman, 2013 and are used with permission (Creative Commons Attribution 3.0 United States License).
Unlike a traditional STEM Calculus I course, this Calculus for Business and Social Sciences course does not teach graphing functions by using function transformations.
Students in this class are expected to make a table of solutions and graph the function. Students will also learn how to graph functions using Calculus!
Graph the following functions:
- \(f(x) = \sqrt[3]{x}\)
- \(f(x) = \dfrac{1 }{x^2 − 3}\)
Solution
- Make a table of solutions and define the domain of the function.
| Table of Solutions for \(f(x) =\sqrt[3]{x}\) Domain \((−\infty , \infty )\) | |
| \(x\) | \(f(x)\) |
| -8 | -2 |
| -1 | -1 |
| 0 | 0 |
| 1 | 1 |
| 8 | 2 |
- Make a table of solutions and define the domain of the function. To identify the domain of this rational function, pay attention to the denominator. The denominator cannot equal 0. Set the denominator = 0 to solve for x and find the values that will not be allowed for x.
\(\begin{aligned} f(x) &= \dfrac{1 }{x^2 − 3}\\ 0 &= x^2 − 3 \\3 &= x^2 \\ \pm \sqrt{3} &=\sqrt{x^2} \\ \pm \sqrt{3}& = x \end{aligned}\)
These numbers need to be excluded from the domain of this function \(−\sqrt{3}\) (about −1.732)) and \(\sqrt{3}\) (about 1.732)).
To correctly graph this function, it’s important to examine the behavior around these numbers that are excluded from the domain. Thus, the reason for so many ordered pairs in the table of solutions. Think of it like this: start with a domain of \((−\infty , \infty )\), but must remove any numbers that will cause problems (like in this case, numbers that will cause the denominator of the function to be 0, because division by 0 is undefined). Graphing functions like this by hand is very tedious, but it’s an important skill for a student to have to succeed in Calculus for Business and Social Sciences.
| Table of Solutions for \(f(x) = \sqrt[3]{ x}\) Domain \((−\infty , \infty )\) | |
| \(x\) | \(f(x)\) |
| -4 | 0.077 |
| -3 | 0.167 |
| -2 | 1 |
| -1.5 | -1.333 |
| -1 | -0.5 |
| -0.5 | -0.364 |
| 0 | 0 |
| 0.5 | -0.364 |
| 1 | -0.5 |
| 1.5 | -1.333 |
| 2 | 1 |
| 3 | 0.167 |
| 4 | 0.077 |
Practice Problems: Graph the following functions, paying attention to the domain of the function.
- \(f(x) = 2x^3\)
- \(f(x) = \dfrac{1 }{2x^2}\)
- \(f(x) = 4 \vert x − 2 \vert\)
- \(f(x) = \dfrac{1 }{3} x − 12 \)
- \(f(x) = \dfrac{1 }{x − 7}\)
- \(f(x) = 3\sqrt{2x^3 + 1}\)


9.1: Introduction
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After completing this section, you should be able to identify substitution and elimination as being the two most important reactions of alkyl halides.
Alkyl halides are electrophiles, which means they can undergo nucleophilic substitution and base-induced elimination reactions. These reaction types offer a large and useful range of reactions for organic synthesis in the laboratory.
Two reactions are shown her with both involving heating a halogenoalkane under reflux with sodium or potassium hydroxide solution. Two different reactions can occur.
The hydroxide ions present are good nucleophiles, and one possibility is a replacement of the halogen atom by an -OH group to give an alcohol via a nucleophilic substitution reaction.
In the example, 2-bromopropane is converted into propan-2-ol.
Hydroxide ions are also strong bases, therefore halogenoalkanes also undergo elimination reactions in the presence of sodium or potassium hydroxide.
In this reaction, the 2-bromopropane has reacted to form an alkene - propene.
Notice that a hydrogen atom has been removed from one of the end carbon atoms together with the bromine from the centre one. In all simple elimination reactions the things being removed are on adjacent carbon atoms, and a double bond is set up between those carbons.
The reagents you are using are the same for both substitution or elimination - the halogenoalkane and either sodium or potassium hydroxide solution. In all cases, you will get a mixture of both reactions happening - some substitution and some elimination. What you get most of depends on a number of factors.


11.8: Review Questions
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1.
Shariq has avoided making an appointment at the college career center and has changed his major four times in his first year. When asked whether he likes his current major, he says, “Sure, but if something better comes along, I’ll switch.” According to James Marcia, at which identity stage is he?
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identity achievement
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identity diffusion
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identity foreclosure
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identity moratorium
2 .
What has been the impact of globalization on cultural values such as collectivism and individualism?
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They have caused intracultural strife, as younger generations seek to maintain the values of their predecessors.
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It has caused many cultures to become wary of and unwelcoming of outsiders to their communities.
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The lines between these cultural values have become less distinct and may, in fact, be outdated.
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It has led to more and more legislation that governs which behaviors are unacceptable within a given culture.
3.
Emerging adulthood is a developmental period that is
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a time where irresponsible decisions and “experience one’s wild side” are regarded as normal and healthy
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rejected as a concept in most collectivistic countries, but is embraced in individualistic cultures
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bound by specific neurological changes rather than specific ages where the period begins and ends
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recognized in some countries as a “buffer” between adolescence and full adulthood
4 .
Unintentional injuries are the leading cause of death during emerging adulthood, and the majority of them are caused by
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overdose on recreational substances
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head injuries during athletic or recreational events
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accidental shootings
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automobile accidents
5.
The American Heart Association recommends that adults get ________ of moderate intensity aerobic activity each week, though this should be spread out over multiple occasions.
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90 minutes
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4 hours
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150 minutes
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1 hour
6 .
Chronic sleep deprivation appears to damage brain tissue in the ________ and ________, producing problems with working memory, attention, and numerical processing.
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thalamus and hypothalamus
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prefrontal cortex and hippocampus
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cerebellum and pons
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amygdala and motor cortex
7.
In a 2021 study by the Urban Institute, which group of individuals was found to have the lowest percentage of children “on track” for healthy developmental outcomes?
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White children
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Native American and Indigenous children
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Hispanic children
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Black children
8 .
The quality and amount of ________, a lubricant that keeps our joints healthy, starts to decline by our 30s, which can lead to join stiffness over time.
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collagen
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lymph
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synovial fluid
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cartilage
9.
The ages at which people are most at risk of contracting an STI are
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20 to 30
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17 to 25
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16 to 22
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18 to 24
10 .
Which STI is caused by a parasite?
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Trichomoniasis
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Syphilis
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Gonorrhea
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Chlamydia
11.
What is the best way to describe the process of “coming out” for people in the LGBTQ+ community?
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It cannot happen until one feels that they will be accepted by their family of origin.
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It involves several tasks that are often experienced sequentially.
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It is the only way an LGBTQ+ person can find inner peace with their sexuality.
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It typically happens after a feeling psychological pressure has built up and must be released all at once.
12 .
Medical conditions that occur more commonly in people with weakened immune systems are called:
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Nosocomial infections
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Iatrogenic conditions
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Opportunistic infections
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Comorbid conditions
13.
Logical thought processes that rely on continuous, active evaluation of information and beliefs using evidence and past experiences are called:
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Social cognition
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Reflective thought
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Crystallized intelligence
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Divergent thinking
14 .
Changes in the brain during emerging adulthood include:
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The end of synaptic pruning, decreased myelination, and more processing of information between more adjacent brain areas
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The beginning of synaptic pruning, decreased myelination, and more processing of information between more distant brain regions
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The beginning of synaptic pruning, increased myelination, and more processing of information between more adjacent brain areas
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The end of synaptic pruning, increased myelination, and more processing of information between more distant brain regions
15.
The ability to draw conclusions about another person’s intentions and beliefs is called:
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Cognitive theory of mind
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Affective theory of mind
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Cognitive altruistic empathy
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Affective altruistic empathy
16 .
Heuristics are best described as
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Pitfalls to problem solving that cause us to get stuck using the same solution repeatedly
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Step-by-step plans for solving problems that always lead to solutions.
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Shortcuts that help us process information more quickly to make decisions
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Paradoxes in thought that cannot be resolved quickly.
17.
Convergent thought uses ________ to deal with a problem.
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a known solution
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new solutions
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help from others
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a solution that works for everyone
18 .
What are the four E’s?
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Enroll, enlist, explore, enjoy
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Enroll, enlist, explore, employment
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Enroll, enlist, enter, employment
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Enroll, enlist, explore, estimate
19.
In the 2021–2022 academic year, the most common major among U.S. college students was
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Business
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Psychology
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Engineering
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Biology
20 .
According to the U.S. Department of Education, approximately what percentage of students enrolled in a two- or four-year degree program change their major before graduating?
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10 percent
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60 percent
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5 percent
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30 percent
21.
Which group of workers tends to feel most positively toward their employer and report the least amount of stress at work?
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Workers with a bachelor’s degree
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Workers with long COVID
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Workers over age 65
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Workers who completed apprenticeship programs before employment
22 .
People with some college but no degree have an unemployment rate ________ than that of people with a bachelor’s degree and ________ than that of people with an associate’s degree.
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Higher; lower
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Lower; lower
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Higher; higher
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Lower; higher


6.1: Overview of Managerial Decision-Making
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exploring managerial careers
Up, Up, and Away: How Stephanie Korey and Jen Rubio founded their luggage company
Jen Rubio and Stephanie Korey faced a number of important decisions in starting their luggage company, Away—beginning with the decision to start a business! That decision came about after Rubio’s luggage broke on a trip. She found it frustrating that all the luggage options were either inexpensive ($100 or less) but low quality, or high quality but incredibly expensive ($400 and above). There was no midrange option. So in 2015 Rubio and her friend Stephanie Korey began researching the luggage industry. They found that much of the reason for the high prices on quality luggage was because of how it was distributed and sold, through specialty retail shops and department stores. If they opted instead for a model in which they sold directly to consumers, they could provide high-quality luggage at more of a midrange ($200-$300) price. After considerable research, the two were convinced that they had an idea worth pursuing. Rubio and Korey settled on the company name “Away,” which is intended to invoke the pleasure that comes from traveling.
Both of the founders had prior experience working for a start-up in the e-commerce space (Warby Parker), which helped them with making sound choices. Rubio’s background was more in branding and marketing, while Korey’s was in operations and supply chain management—so each was able to bring great expertise to various aspects of the business. They raised money initially from friends and family, but within a few months, they sought venture capital funding to ensure that they had enough money to get off to a successful start.
A big decision that Rubio and Korey had to make fairly early in the process of establishing their business was to settle on an initial design for the product. This decision required extensive marketing and consumer research to understand customer needs and wants. They asked hundreds of people what they liked about their existing luggage, and what they found most irritating about their existing luggage. They also contracted with a two-person design team to help create the first prototype. This research and development ultimately led to the design of an attractive hard case that is surprisingly lightweight. It also boasts extremely high-quality wheels (four of them, not two) and high-quality zippers. As a bonus, the carry-on includes a built-in battery for charging phones and other devices.
The two founders also had to choose a partner to manufacture their product. Because their product had a hard, polycarbonate shell, Rubio and Korey discovered that manufacturing in the United States was not a viable option—the vast majority of luggage manufacturers using a polycarbonate shell were based in Asia. They researched a number of possible business partners and asked lots of questions. In addition, they eventually visited all of the factories on their list of options to see what they were actually like. This was an important piece of research because the companies that looked best on paper didn’t always turn out to be the best when they visited in person. Rubio and Korey ended up working with a manufacturing partner in China that also produces luggage for many high-end brands, and they have been extremely pleased with the partnership. They continue to devote time to building and maintaining that relationship, which helps to avoid issues and problems that might otherwise come up.
By the end of 2015, Rubio and Korey had developed their first product. Because the luggage was not going to be available in time for the holiday shopping season, they decided to allow customers to preorder the luggage. To drum up interest, the duo engaged in a unique storytelling effort. They interviewed 40 well-respected members of the creative community about their travel experiences and created a hardcover book of travel memoirs called The Places We Return To . Not only was the book interesting and engaging, but it also made lots of people in the creative community aware of Away luggage. Starting in November 2015, the travel memoir book was available for free with the purchase of a gift card that could be redeemed in February 2016 for luggage. The book project generated tremendous advance interest in the product, and the 1,200 printed copies sold out. Away generated $12 million in first-year sales.
Stephanie Corey and Jen Rubio faced many important and novel decisions in initially developing and building their business. They have been successful in part because they made those decisions wisely—by relying on shared knowledge, expertise, and lots of research before reaching a decision. They will continue to face many decisions, big and small. They have expanded their product line from one piece of luggage to four, with more luggage—and other travel accessories—in the works for the future. Their company, which is based in New York, has grown to over 60 employees in the first two years. These employees include the two design-team members who were contracted to help create their first prototype; Rubio and Korey appreciated working with them so much, they offered them full-time positions with Away. Each new hire represents new decisions—decisions about what additional work needs to be done and who they should hire to do it. Each new product also brings additional decisions—but it seems Rubio and Korey have positioned themselves (and their business) well for future successes.
Sources: Kendall Baker, “An Interview With the Co-Founder of Away,” The Hustle , December 5, 2016, https://thehustle.co/episodes ; Bond Street Blog, “Up and Away,” Bond Street , https://bondstreet.com/blog/jen-rubio-interview/ ; Josh Constine, “Away nears 100k stylish suitcases sold as it raises $20M,” TechCrunch , May 19, 2017, https://techcrunch.com/ ; Adeline Duff, “ The T&L Carry-On: Away Travel Co-Founders Jen Rubio and Stephanie Korey,” Travel & Leisure, March 9, 2017, http://www.travelandleisure.com/ ; Burt Helm, “How This Company Launched With Zero Products –and Hit $12 Million in First-Year Sales,” Inc.com , July/August 2017, https://www.inc.com/ ; Veronique Hyland, “The Duo Trying to Make Travel More Glamorous,” The Cut , December 22, 2015, https://www.thecut.com/ .
Managers and business owners—like Jen Rubio and Stephanie Korey—make decisions on a daily basis. Some are big, like the decision to start a new business, but most are smaller decisions that go into the regular running of the company and are crucial to its long-term success. Some decisions are predictable, and some are unexpected. In this chapter, we look at important information about decision-making that can help you make better decisions and, ultimately, be a better manager.
- What are the basic characteristics of managerial decision-making?
Decision-making is the action or process of thinking through possible options and selecting one.
It is important to recognize that managers are continually making decisions and that the quality of their decision-making has an impact—sometimes quite significant—on the effectiveness of the organization and its stakeholders . Stakeholders are all the individuals or groups that are affected by an organization (such as customers, employees, shareholders, etc.).
Members of the top management team regularly make decisions that affect the future of the organization and all its stakeholders, such as deciding whether to pursue a new technology or product line. A good decision can enable the organization to thrive and survive long-term, while a poor decision can lead a business into bankruptcy. Managers at lower levels of the organization generally have a smaller impact on the organization’s survival, but can still have a tremendous impact on their department and its workers. Consider, for example, a first-line supervisor who is charged with scheduling workers and ordering raw materials for her department. Poor decision-making by lower-level managers is unlikely to drive the entire firm out of existence, but it can lead to many adverse outcomes such as:
- reduced productivity if there are too few workers or insufficient supplies,
- increased expenses if there are too many workers or too many supplies, particularly if the supplies have a limited shelf life or are costly to store, and
- frustration among employees, reduced morale and increased turnover (which can be costly for the organization) if the decisions involve managing and training workers.
Deciding When to Decide
While some decisions are simple, a manager’s decisions are often complex ones that involve a range of options and uncertain outcomes. When deciding among various options and uncertain outcomes, managers need to gather information, which leads them to another necessary decision: how much information is needed to make a good decision? Managers frequently make decisions without complete information; indeed, one of the hallmarks of an effective leader is the ability to determine when to hold off on a decision and gather more information, and when to make a decision with the information at hand. Waiting too long to make a decision can be as harmful for the organization as reaching a decision too quickly. Failing to react quickly enough can lead to missed opportunities, yet acting too quickly can lead to organizational resources being poorly allocated to projects with no chance of success. Effective managers must decide when they have gathered enough information and must be prepared to change course if additional information becomes available that makes it clear that the original decision was a poor one. For individuals with fragile egos, changing course can be challenging because admitting to a mistake can be harder than forging ahead with a bad plan. Effective managers recognize that given the complexity of many tasks, some failures are inevitable. They also realize that it’s better to minimize a bad decision’s impact on the organization and its stakeholders by recognizing it quickly and correcting it.
What’s the Right (Correct) Answer?
It’s also worth noting that making decisions as a manager is not at all like taking a multiple-choice test: with a multiple-choice test, there is always one right answer. This is rarely the case with management decisions. Sometimes a manager is choosing between multiple good options, and it’s not clear which will be the best. Other times there are multiple bad options, and the task is to minimize harm. Often there are individuals in the organization with competing interests, and the manager must make decisions knowing that someone will be upset no matter what decision is reached.
What’s the Right (Ethical) Answer?
Sometimes managers are asked to make decisions that go beyond just upsetting someone—they may be asked to make decisions in which harm could be caused to others. These decisions have ethical or moral implications. Ethics and morals refer to our beliefs about what is right vs. wrong, good vs. evil, virtuous vs. corrupt. Implicitly, ethics and morals relate to our interactions with and impact on others—if we never had to interact with another creature, we would not have to think about how our behaviors affected other individuals or groups. All managers, however, make decisions that impact others. It is therefore important to be mindful of whether our decisions have a positive or a negative impact. “Maximizing shareholder wealth” is often used as a rationalization for placing the importance of short-term profits over the needs of others who will be affected by a decision—such as employees, customers, or local citizens (who might be affected, for example, by environmental decisions). Maximizing shareholder wealth is often a short-sighted decision, however, because it can harm the organization’s financial viability in the future. 1 Bad publicity, customers boycotting the organization, and government fines are all possible long-term outcomes when managers make choices that cause harm in order to maximize shareholder wealth. More importantly, increasing the wealth of shareholders is not an acceptable reason for causing harm to others.
As you can see from these brief examples, management is not for the faint of heart! It can, however, be incredibly rewarding to be in a position to make decisions that have a positive impact on an organization and its stakeholders. We see a great example of this in the Sustainability and Responsible Management box.
SUSTAINABILITY AND RESPONSIBLE MANAGEMENT
Brewing Sustainable Success
The focus of a manager or a business owner is often primarily on doing well (making a profit). Sometimes, though, organizational leaders choose to pursue two big goals at once: doing well and simultaneously doing good (benefiting society in some way). Why? Generally, because they think it’s an important thing to do. The business provides an opportunity to pursue another goal that the founders, owners, or managers are also passionate about. In the case of New Belgium Brewing, the company’s cofounders, Jeff Lebesch and Kim Jordan were passionate about two things: making great beer and environmental stewardship. So it should come as no surprise that their brewery is dedicated to reducing its environmental footprint. The brewery has created a culture that fosters sustainability in a wide range of ways, such as by giving employees a bicycle on their one-year anniversary as a way to encourage them to ride bicycles to work. The organization is also active in advocacy efforts, such as the “Save the Colorado” (river) campaign, and it works hard to promote responsible decision-making when it comes to environmental issues. In fact, in 1999, following an employee vote, the brewery began to purchase all of its electricity from wind power, even though it was more expensive than electricity from coal-burning power plants (which meant reduced profitability and less money for employee bonuses).
While the brewery still relies primarily on wind power, it also now generates a portion of its electricity onsite—some from rooftop solar panels, and even more from biogas, the methane gas byproduct that is created by microbes in the brewery’s water treatment plant. The company cleans the wastewater generated from beer production, and in doing so it generates the biogas, which is captured and used for energy to help run the brewery.
Brewing is water-intensive, so New Belgium works hard to reduce water consumption and to recycle the water that it does use. The company also reduces other types of waste by selling used grain, hops, and yeast to local ranchers for cattle feed. The company, which has been employee-owned since 2013, also works with the local utility through a Smart Meter program to reduce its energy consumption at peak times.
All of these efforts at doing good must come at a cost, right? Actually, research shows that companies that are committed to sustainability have superior financial performance, on average, relative to those that are not. In coming up with creative ways to reduce, reuse, and recycle, employees often also find ways to save money (like using biogas). In addition, organizations that strive to do good are often considered attractive and desirable places to work (especially by people who have similar values) and are also valued by the surrounding communities. As a result, employees in those organizations tend to be extremely committed to them, with high levels of engagement, motivation, and productivity. Indeed, it seems clear that the employees at the New Belgium Brewery are passionate about where they work and what they do. This passion generates value for the organization and proves that it is, in fact, possible to do well while having also made the decision to do good. And in the case of New Belgium Brewery, that means working to protect the environment while also making delicious beer.
Discussion Questions:
- What challenges does New Belgium Brewery face in pursuing environmental goals?
- Can you think of any other examples of companies that try to “do good” while also doing well?
- Would you like to work for an organization that is committed to something more than just profitability, even if it meant your salary or bonus would be smaller?
Sources: Karen Crofton, “How New Belgium Brewery leads Colorado’s craft brewers in energy,” GreenBiz , August 1, 2014, https://www.greenbiz.com/ . Darren Dahl, “How New Belgium Brewing Has Found Sustainable Success,” Forbes , February 8, 2016, https://www.forbes.com/ . Jenny Foust, “New Belgium Brewing Once Again Named Platinum-Level Bicycle Friendly Business by the League of American Bicyclists,” Craft Beer.com, February 18, 2016. Robert G. Eccles, Ioannis Ioannou, & George Serafeim, “The Impact of Corporate Sustainability on Organizational Processes and Performance,” Management Science , 60, 2014, https://doi.org/10.1287/mnsc.2014.1984 . New Belgium Brewery Sustainability web page, http://www.newbelgium.com/sustainability , accessed September 18, 2017.
concept check
- What are some positive outcomes of decision-making for an organization? What are some possible negative outcomes?
- How is managerial decision-making different from a multiple-choice test?
- In addition to the owners of a business, who are some of the other stakeholders that managers should consider when making decisions?


23.4: The Qin Dynasty
The Qin Dynasty
The Qin Dynasty (221-206 BCE), though short-lived, is remembered for its military strength and its unification of China.
Describe the establishment of the first imperial dynasty of China and the architecture, literature, weaponry, and sculpture it produced
Key Points
- In the mid and late 3rd century BCE, the Qin accomplished a series of swift conquests, eventually gaining control over the whole of China and creating a unified nation.
- During its reign , the Qin Dynasty achieved increased trade, improved agriculture, and revolutionary developments in military tactics, transportation, and weaponry, such as the sword and crossbow.
- The Dynasty is known for several impressive feats in architecture, sculpture, and other art, such as the beginnings of the Great Wall of China, the construction of the Terracotta Army, and the standardization of the writing system.
Key Terms
- Qin Shihuang : The self-proclaimed first Emperor of the Qin Dynasty.
- Warring States Period : A period in ancient China following the Spring and Autumn period and concluding with the victory of the state of Qin in 221 BCE, creating a unified China under the Qin Dynasty.
- legalism : A philosophy of focusing on the text of written law to the exclusion of the intent of law, elevating strict adherence to law over justice, mercy, grace and common sense.
History: The Qin Dynasty
The Qin Dynasty was the first imperial dynasty of China, lasting only 15 years from 221 to 206 BCE. The strength of the Qin state was greatly increased by the legalist reforms of Shang Yang in the 4 th century BCE, during the Warring States Period . Legalism is a philosophy of focusing on the text of written law to the exclusion of the intent of law, elevating strict adherence to law over justice, mercy, grace, and common sense. In the mid and late 3rd century BCE, the Qin accomplished a series of swift conquests, first ending the powerless Zhou Dynasty and eventually destroying the remaining six of the major states, thus gaining control over the whole of China. This resulted in the first-ever unified China.
Accomplishments of the Qin Dynasty
During its reign over China, the Qin Dynasty achieved increased trade, improved agriculture, and revolutionary developments in military tactics, transportation, and weaponry. Qin Shihuang , the self-proclaimed first Emperor of the Qin Dynasty, made vast improvements to the military, which used the most advanced weaponry of its time. The sword was invented during the previous Warring States Period, first made of bronze and later of iron. The crossbow had been introduced in the 5th century BCE and was more powerful and accurate than the composite bows used earlier; it could also be rendered ineffective by removing two pins, which prevented enemies from capturing a working crossbow.
The Dynasty is also known for many impressive feats in architecture, sculpture, and other art, such as the beginnings of the Great Wall of China, the construction of the Terracotta Army, and the standardization of the writing system.
Decline of the Dynasty
Despite its military strength, however, the Dynasty did not last long. When Qin Shihuang died in 210 BCE, his son was placed on the throne by two of the previous emperor’s advisers, who attempted to influence and control the administration of the entire dynasty through him. The advisers fought among themselves, however, which resulted in both their deaths and that of the second Qin emperor. Popular revolt broke out a few years later, and the weakened empire soon fell to a Chu lieutenant, who went on to found the Han Dynasty. Despite its rapid end, the Qin Dynasty influenced future Chinese empires, particularly the Han, and the European name for China is thought to be derived from it.
Architecture of the Qin Dynasty
Qin architecture is characterized by defensive structures and elements that conveyed authority and power, as exemplified by the early beginnings of the Great Wall.
Examine the characteristics of architecture created under the Qin Dynasty
Key Points
- Architecture from the previous Warring States Period had several definitive aspects which carried into the Qin Dynasty .
- City walls used for defense were made longer, and secondary walls were often built to separate the different districts.
- Versatility in federal structures was emphasized to create a sense of authority and absolute power, conveyed by architectural elements such as high towers, pillar gates, terraces, and high buildings.
- Qin Shihuang , the self-proclaimed first Emperor, is responsible for the initial construction of what later became the Great Wall of China, which he built along the northern border to protect his empire against the Mongols .
Key Terms
- Qin Shihuang : The self-proclaimed first Emperor of the Qin Dynasty.
- Great Wall of China : A series of fortifications made of stone, brick, tamped earth, wood, and other materials, generally built along an east-to-west line across the historical northern borders of China to protect the Chinese states and empires against the raids and invasions of the nomadic groups of the Eurasian Steppe.
The Qin Dynasty was the first imperial dynasty of China, lasting from 221 to 206 BCE. The Dynasty followed the Warring States Period and resulted in the unification of China, ending 15 years later with the introduction of the Han Dynasty.
Architecture from the Warring States Period had several definitive aspects which carried into the Qin Dynasty. City walls used for defense were made longer, and secondary walls were often built to separate the different districts. Versatility in federal structures was emphasized to create a sense of authority and absolute power, conveyed by architectural elements such as high towers, pillar gates, terraces, and high buildings.
The Beginnings of the Great Wall
During its reign over China, the Qin sought to create an imperial state unified by highly structured political power and a stable economy able to support a large military. The Qin central government minimized the role of aristocrats and landowners to have direct administrative control over the peasantry, who comprised the overwhelming majority of the population and thus made up a large labor force. This allowed for the construction of ambitious projects such as the wall on the northern border now known as the Great Wall of China.
Qin Shihuang, the first self-proclaimed emperor of the Qin Dynasty, developed plans to fortify the northern border against the nomadic Mongols. The result was the initial construction of what later became the Great Wall of China, built by joining and strengthening the walls made by the feudal lords. These were expanded and rebuilt multiple times by later dynasties, also in response to threats from the north.
Literature of the Qin Dynasty
Under the Qin Dynasty, a standardized system of Chinese writing was created. This unified Chinese culture for thousands of years.
Discuss the goals of literature produced during the Qin Dynasty
Key Points
- Prime Minister Li Si standardized the writing system across the whole country. This unified Chinese culture for thousands of years.
- Li Si is credited with creating the “lesser-seal” style of calligraphy , also known as small seal script. This served as a basis for the modern Chinese writing system and is still used in cards, posters, and advertising today.
- In 221 BC, Qin Shihuang , the first Qin emperor, conquered all of the Chinese states and governed with a single philosophy known as legalism . This encouraged severe punishments, particularly when the emperor was disobeyed.
- An attempt to purge all traces of the old dynasties and their philosophies led to the infamous burning of books and burying of scholars incident in 213 BCE.
- In an attempt to consolidate power, Qin Shihuang ordered the burning of all books on non-legalist philosophical viewpoints and intellectual subjects; scholars who refused to submit their books were executed.
Key Terms
- logographic : A writing system based on characters that represent a word or phrase, such as Chinese characters, Japanese kanji, and some Egyptian hieroglyphs.
- legalism : A philosophy focusing on the text of written law to the exclusion of the intent of law, elevating strict adherence to law over justice, mercy, grace, and common sense.
Li Si and the Standardization of Writing
The written language of the Qin Dynasty (221-206 BCE) was logographic like that of the Zhu; each written character represented a word or phrase, as opposed to letters as in the English alphabet. As one of his most influential achievements, prime minister Li Si of the Qin Dynasty standardized the writing system to be of uniform size and shape across the whole country. This had a unifying effect on Chinese culture that lasted thousands of years. Li Si is also credited with creating the “lesser-seal” style of calligraphy, also known as small seal script. This served as a basis for the modern Chinese writing system and is still used in cards, posters, and advertising today.
Before the Qin conquest of the last six of the Warring States of Zhou China, local styles of characters evolved independently for centuries, producing what are called the “Scripts of the Six States” or “Great Seal Script”. Under one unified government however, the diversity was deemed undesirable as it hindered timely communication, trade, taxation, and transportation. In addition, independent scripts could express dissenting political ideas.
As a result, coaches, roads, currency, laws, weights, measures, and writing were systematically unified under the Qin. Characters different than those found in Qin were discarded, and Li Si’s small seal characters became the standard for all regions within the empire. This policy came into effect around 220 BCE, the year after Qin’s unification of the Chinese states, and was introduced by Li Si and two ministers.
The Burning of Books
One of the more drastic measures to eradicate the old schools of thought during the Qin Dynasty was the infamous burning of books and burying of scholars incident. This decree, passed in 213 BCE, almost single-handedly gave the Qin Dynasty a bad reputation in history. In an attempt to consolidate power, Qin Shihuang ordered the burning of all books on non-legalist philosophical viewpoints and intellectual subjects. All scholars who refused to submit their books were executed. As a result, only texts considered productive by the legalists (largely discussing pragmatic subjects such as agriculture, divination, and medicine) were preserved.
A Consolidation of Power
During the previous Warring States period, the Hundred Schools of Thought comprised many philosophies proposed by Chinese scholars, including Confucianism . In 221 BC, Qin Shihuang, the first Qin emperor, conquered all of the Chinese states and governed with a single philosophy known as legalism. This encouraged severe punishments, particularly when the emperor was disobeyed. Individuals’ rights were devalued when they conflicted with the government’s or the ruler’s wishes, and merchants and scholars were considered unproductive and fit for elimination. During the dynasty, Confucianism—along with all other non-legalist philosophies—was suppressed by the First Emperor.
Sculpture of the Qin Dynasty
The Qin Dynasty is perhaps best known for the impressive Terracotta Army, built to protect Qin Shihuang in the afterlife.
Evaluate the sculpture of the Qin Dynasty
Key Points
- The Qin, under the leadership of emperor Qin Shihuang , accomplished a series of swift conquests and gained control over all of China, unifying it as a country for the first time.
- The Qin made many advancements in sculpture during their short reign, building on techniques practiced by the previous Zhou Dynasty .
- The most famous example of sculpture under the Qin Dynasty was a project commissioned during Qin Shihuang’s rule known as the Terracotta Army, intended to protect the emperor after his death.
- The Terracotta Army consists of more than 7,000 life-size terracotta figures of warriors and horses, buried with Qin Shihuang after his death in 210–209 BCE.
- Originally, the figures were painted with bright pigments of pink, red, green, blue, black, brown, white, and lilac; however, much of the color coating flaked off or faded.
- The figures were constructed in several poses, including standing infantry, kneeling archers, and charioteers with horses.
Key Terms
- terracotta : A type of earthenware, clay-based unglazed or glazed ceramic, in which the fired body is porous.
- Qin Shihuang : The self-proclaimed first Emperor of the Qin Dynasty.
The Qin Dynasty was the first imperial dynasty of China, lasting from 221 to 206 BCE. The Dynasty followed the Warring States Period and ended after only 15 years with the Han Dynasty. The Qin, under the leadership of its first self-proclaimed emperor Qin Shihuang, accomplished a series of swift conquests, first ending the powerless Zhou Dynasty and eventually destroying the remaining six of the major states and gaining control of all of China. Under the Qin, it was unified as a country for the first time. The Qin made many advancements in sculpture during their short reign, building on techniques practiced by the previous Zhou Dynasty.
The Terracotta Army
The most famous example of sculpture under the Qin Dynasty was a project commissioned during Qin Shihuang’s rule known as the Terracotta Army, intended to protect the emperor after his death. The Terracotta Army was inconspicuous due to its underground location and thus not discovered until 1974. The “army” of sculptures consists of more than 7,000 life-size terracotta figures of warriors and horses that were buried with Qin Shihuang after his death in 210–209 BCE. The three pits containing the Terracotta Army were estimated in 2007 to hold more than 8,000 soldiers, 130 chariots with 520 horses, and 150 cavalry horses, the majority of which remained buried in the pits nearby Qin Shi Huang’s mausoleum . Non-military terracotta figures were found in other pits, including officials, acrobats, strongmen, and musicians.
Style of the Figures
The figures were painted in bright pigments before they were placed in the vault , and the original colors of pink, red, green, blue, black, brown, white, and lilac were visible when the pieces were first unearthed. However, exposure to air has caused the pigments to fade and flake off, revealing their natural terracotta color. The figures were constructed in several poses, including standing infantry, kneeling archers, and charioteers with horses. They vary in height according to their roles, with the generals tallest, and each figure’s head appears to be unique, with a variety of facial features, expressions, and hair styles. Along with the colored lacquer finish, the individual facial features would have given the figures a realistic feel.
Construction
The terracotta army figures were manufactured in workshops by government laborers and local craftsmen using local materials. Heads, arms, legs, and torsos were created separately and then assembled. Eight face molds were most likely used, with clay added after assembly to provide individual facial features. It is believed that the legs were made using the same process used for terracotta drainage pipes. This would classify the process as assembly line production, with specific parts manufactured and assembled after being fired, as opposed to being crafted from one solid piece and subsequently fired. In those times of tight imperial control, each workshop was required to inscribe its name on items produced to ensure quality control.
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