3.3: More on Compounding Interest and Continuous Exponential Models
Focus: More on Compound Interest
Many types of bank accounts utilize compound interest, such as a bank certificates of deposit (CD), savings accounts, and credit cards. The term \(compounding\) comes from the behavior that interest is earned not only on the original value, but on the accumulated value of the account. The time period, or \(compounding\) \(period\), over which interest is calculated may differ by the account. In one CD, interest could be calculated every month (such as 2% interest per month) whereas in another interest could be can calculated every year (such as 12% per year). In order to compare interest rates compounded over different time periods, interest rates are usually expressed as a nominal rate or an annual percentage rate (APR) . Let's explore an example to understand how this effects how we calculate interest.
The annual percentage rate (APR) of an investment is the percentage of interest gained on the original principal, or amount invested, over a year.
You invest $1,000 into an investment account that pays a 6% APR (annual percentage rate) of interest.
a) If you compounded interest annually (or once per year), how much will be in the account in a year?
b) If you compounded interest quarterly, how much will be in the account in a year?
Solution
a) Since we are starting with $1,000, our initial value \(a = 1000\).
Our annual interest rate is 6%, so \(r = 0.06\), and our growth factor b = 100% + 6% =106% as a percent or b =1 +0.06 = 1.06 as a decimal. Each time we compound interest, we multiply the previous amount by our growth factor b = 1.06.
So in one year, we will have
\[A(1)=1000(1.06)^{1} =\$ 1060.\nonumber\]
b) Since we are compounding quarterly, we are compounding 4 times per year and need to break the annual interest rate into 4 parts. So the interest per quarter is \(r = \dfrac{6}{4}\) = 1.5% as a percent or as a decimal \(r = \dfrac{.06}{4}\) = 0.015.
So our quarterly growth factor b = 100% + 1.5% =101.5% as a percent or b =1 +0.015=1.015 as a decimal. Each time we compound interest, we multiply the previous amount by our growth factor b = 1.015.
So in one year, we will have
\[A(1)=1000(1.015)^{4} =\$ 1061.36.\nonumber\]
Can you explain why more interest is gained when we compounded interest quarterly? In the first quarter, we gained $15 in interest since
\[A=1000(1.015)^{1} =\$ 1015.\nonumber\]
In the second quarter, we gained interest on the original principal($1000) plus the first month's interest ($15). The interest on the original principal=\(1000(.015)=$15\) and the interest on the first months interest \((15)(.015)=$0.225\). More interest was gained in the second quarter, \(15+0.225=$15.225\) than the first quarter, since we are gaining interest on previous interest as well as the original principal.
When the interest is compounded more frequently than once a year, the account effectively earns more that the nominal rate or APR. We call this rate the account actually earned the \(effective\) \(annual\) \(rate\).
The effective annual rate is the percentage rate r that an account actually increased by over a year incorporating the effects of compounding interest.
In example 3.3.1 part b, the effective annual rate was \(r =\dfrac{61.36}{1000} = 0.06136\) or \(6.136\)%. Notice, that we could have obtained this by using the growth factor. After compounding four times, the account grows by a factor of \(b^{4}=(1.015)^{4}=1.06136.\) As a percent, the account is 106.136% or the original amount after a year. It has grown by 6.136%.
Example \(\PageIndex{2}\)
A 529 plan is a college savings plan in which a relative can invest money to pay for a child’s later college tuition. The account grows tax free. Lily wants to set up a 529 account for her new granddaughter so that the account grows to $40,000 over 18 years. She believes the account will earn a 4% APR compounded semi-annually (twice a year).
a) How much will Lily need to invest in the account?
b) What is the effective annual rate of her account?
Solution
a) Since the account is earning a 4% APR, the interest per compounding period (semi-annually)is r = \(\dfrac{4}{2}\)=2% or as a decimal r = \(\dfrac{0.04}{2}=0.02\) as a decimal.
Then the growth factor per period (semi-annually) is b = 100% + 2% =102% as a percent or b = 1 +0.02 = 1.02 as a decimal. Each time interest is compounded, we multiply the previous amount by our growth factor b = 1.02. The account will be compounding twice a year for 18 years, so the number of compoundings n = (18)(2) =36.
In this problem, we don’t know how much we are starting with, so we will be solving for a, the initial amount. We do know that we want the end amount to be $40,000. We want for the value of a so that \(A(18) = 40,000\).
\[\begin{array}{l} {40,000=A(18)=a(1.02)^{36} } \\ {40,000=a(2.039887)} \\ {a=\dfrac{40,000}{2.039887} \approx \$ 19,608.93} \end{array}\nonumber \]
Lily will need to invest $19,608.93 to have $40,000 in 18 years.
b) In one year, the account will compound twice. So we will multiply our initial amount by our growth factor twice \(b^{2}=1.02^{2}=1.0404\). Effectively our account will be 104.04% of the initial value. So the effective annual rate is 4.04%.
Student Exercise \(\PageIndex{1}\)
You owe $5000 on a credit card that charges a 12% APR of interest compounded monthly.
a) Find a formula for the amount owed, A, after t years if no payments are made.
b) Predict the amount owed in 5 years.
c) What is the effective annual rate of the credit card account?
- Answer
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a) Since the account is earning a 12% APR, the interest per month is r = \(\dfrac{12}{12}\)=1% as a percent or as a decimal r = \(\dfrac{0.12}{12}=0.01\) as a decimal. Then the growth factor per month is b = 100% + 1% =101% as a percent or b = 1 +0.01 = 1.01 as a decimal. Each time we compound interest, we multiply the previous amount by our growth factor b = 1.01.
The account will be compounding twelve times a year for t years. So the number of compoundings in t years is n = (12)(t) =12t.
The initial value, or principal, \(a=5000\). So a formula for the amount owed after t years is
\[A=A(t)=5000(1.01)^{12t} \nonumber\]
b) In 5 years, t = 5. So the amount in the owed will be
\[A=A(5)=5000(1.01)^{12(5)} = $9,083.48 \nonumber\]
c) In one year, the account will compound 12 times. So the initial amount will be multiplied by our growth factor b = 1.01 twelve times and increase by a factor of = \(b^{12}=(1.01)^{12}\approx 1.126825\). Effectively, the credit card debt will be 112.6825% of the initial value. So the effective annual rate is 12.6825%.
Generalizing this, we can form a general formula for compound interest. If the APR is written in decimal form as \(r\), and there are \(k\) compounding periods per year, then the interest per compounding period will be \(\dfrac{r}{k}\). So the growth factor per period will be b=\((1+\dfrac{r}{k})\). Likewise, if we are interested in the value after \(t\) years, then there will be \(n=kt\) compounding periods in that time.
Compound Interest can be calculated using the formula
\[A(t)=a\left(1+\dfrac{r}{k} \right)^{kt}\]
Where \(A(t)\) is the account value
- \(t\) is measured in years
- \(a\) is the starting amount of the account, often called the principal
- \(r\) is the annual percentage rate (APR), also called the nominal rate, written as a decimal
- \(k\) is the number of compounding periods in one year
Bank A offers an account paying 1.2% compounded quarterly. Bank B offers an account paying 1.1% compounded monthly. Which bank is offering a better rate?
- Answer
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We can compare these rates using the effective annual percentage rate, the actual percent increase per year.
Bank A has a quarterly interest rate of r = \(\dfrac{0.012}{4}=0.003\) as a decimal. The growth factor per quarter is \(b=1+ 0.003=1.003\). In one year, the account will compound 4 times and grow by a factor of \(b^{4} =1.003^{4} \approx 1.012085411\). Therefore, the account will be<PHONE_NUMBER>% of the initial value. So the effective annual rate is 1.2085411%.
Bank B has a monthly interest rate of r = \(\dfrac{0.011}{12}=0.0009166667\) as a decimal. The growth factor per month is \(b=1+ 0.0009166667=1.0009166667\). In one year, the account will compound 12 times and grow by a factor of \(b^{12} =1.0009166667^{12} \approx 1.011661873\). Therefore, the account will be<PHONE_NUMBER>% of the initial value. So the effective annual rate is 1.1661873%.
Bank B’s monthly compounding is not enough to catch up with Bank A’s better APR. Bank A offers a better rate.
Focus: Periodic Exponential Growth versus Continuous Exponential Growth
Compounding interest is an example of periodic exponential growth , where the growth occurs at the end of a time period, such as 6% per year or 3% per quarter. Many other exponentially growing (or decaying) quantities grow (or decay) continuously through the time period. For example, the difference in temperature between a hot cup of coffee and its ambient environment decreases at every instant, not just at the end of the time period. Exponential growth (or decay) that occurs continuously through a time period is called continuous exponential growth (or decay) . The population growth of a country is another example of continuous exponential growth since the growth in the number of people occurs continuously through the year not just at the end of the year. Be aware that we may communicate the growth of a continuously growing exponential quantity with a periodic growth rate, such as the population of a country growing by 1.12% per year. The exponential growth formula we have been working with so far, \(y=a(b)^{x}\), is related to the periodic growth rate. For example, if a quantity grows by 1.12% per year, the growth factor would be b = 100% + 1.12% = 101.12% as a percent or b = 1 + 0.0112 = 1.0112 as a decimal. For this reason, we call this the periodic exponential growth (or decay) formula.
Periodic Exponential Growth can be calculated using the formula
\[f(x)=ab^{x}\]
where
\(a\) is the starting amount,
\(r\) is the periodic growth rate written as a decimal,
and \(b\) is the growth factor where b = 1+ r.
How are periodic and continuous exponential growth related? Let's explore what happens to an account with compounded interest, which experiences periodic exponential growth, as we increase the frequency of the compoundings from yearly to quarterly to monthly to daily to hourly to every second as we approach continuous exponential growth. As we saw earlier, the amount we earn increases as we increase the compounding frequency. If we continue to increase the frequency of the compoundings, will the amount we earn keep increasing without bound or eventually level off? The table below shows that the increase from annual to quarterly compounding is larger than the increase from monthly to daily compounding. This might lead us to believe that, although increasing the frequency of compounding will increase our result, there is an upper limit to this process.
To see this, let us examine the value of $1000 invested at 6% interest for 10 years.
| Frequency | Interest per Period, r | Growth Factor per Period, b | Number of Compoundings in 10 years, n |
Amount in 10 years \[A=a(b)^{n} \nonumber \] |
|---|---|---|---|---|
| Annual | \(\dfrac{0.06}{1}=0.06\) | 1+0.06=1.06 (106%) | 10(1)=10 |
\(A=1000(1.06)^{10} \\ = 1790.85 \) |
| Quarterly | \(\dfrac{0.06}{4}=0.015\) | 1+0.015=1.015 | 10(4)=40 |
\(A=1000(1.015)^{40} \\ = 1814.02\) |
| Monthly | \(\dfrac{0.06}{12}=0.005\) | 1+ 0.005 = 1.005 | 10(12)=120 |
\(A=1000(1.005)^{120} \\ = 1819.40\) |
| Daily | \(\dfrac{0.06}{365}\approx0.000164384\) | 1.000164384 | 10(365)=3,650 | \(A=1000(1.000164384)^{3,650} \\=1822.03\) |
| Hourly | \(\dfrac{0.06}{8760}\approx0.0000068493\) | 1.0000068493 | 10(8760)=87,600 | \(A=1000(1.0000068493)^{87,600} \\=1822.11\) |
| Once per minute | 1822.12 | |||
| Once per second | 1822.12 |
These values do indeed appear to be approaching an upper limit of approximately $1822.12 as we approach continuous exponential growth with growth at each instant. In order to describe what this limiting value, we need to introduce a special number, which is so important that it gets represented by its own letter.
Definition: Euler's number: \(e\)
\(e\) is the letter used to represent the value that \(\left(1+\dfrac{1}{k} \right)^{k}\) approaches as \(k\) gets bigger and bigger.
\[e \approx 2.718282\nonumber\]
The number is also called the natural base.
\(e\) is a number that arises in continuous exponential growth similar to how number \(\pi\) arises when dealing with circles. Notice, that the limiting amount in our interest example can be expressed with \(e\).
\[A=1000(e)^{(0.06)(10)} \approx 1822.11\nonumber\]
Notice, the significance of each of the parameters in this equation: the initial value a = 1000, the time t = 10 years, and the percent increase r = 0.06. In this case, r = 0.06 = 6% is the continuous growth rate since growth is occurring at each instant.
In general, a continuously growing (or decaying) exponential quantity can be represented by the following formula.
Definition: Continuous Exponential Growth Formula
Continuous Exponential Growth can be calculated using the formula
\[f(t)=ae^{rt}\]
where
\(a\) is the starting amount,
\(r\) is the continuous growth rate written as a decimal,
and \(t\) is the time.
This type of equation is commonly used when describing quantities that change more or less continuously, like chemical reactions, growth of large populations, and radioactive decay. In general, we can model an exponential quantity with either the periodic or continuous growth formulas, so y = \(ab^{t}=ae^{rt}\) where \(b=e^{r}\). However, we will see that there are some distinct advantages to using the continuous exponential models in some cases in section 3.4.
Example \(\PageIndex{3}\)
A virus is detected with 120 people infected initially and is spreading rapidly.
a) If the number of people infected is increasing by 25% per month, find a formula for the number of people infected, I, in t months. Then predict the number infected in 6 months.
b) If the number of people infected is increasing continuously by 25%, find a formula for the number of people infected, I, in t months. Then predict the number infected in 6 months.
Solution
a) In this scenario, we are given the periodic growth rate r = 25% = 0.25. Therefore, we should use the periodic exponential growth formula \(I = f(t) = ab^{t}\), where a = 120 and b = 100% + 25% = 125% as a percent or b = 1.25 as a decimal. So the number of people infected is given by
\[I=120(1.25)^{t}\nonumber\]
The number infected in 6 months is \(I=120(1.25)^{6}\approx 458\).
b) In this scenario, we are given the continuous growth rate r = 25% = 0.25. Therefore, we should use the continuous exponential growth formula \(I=ae^{rt}\), where a = 120. So the number of people infected is given by
\[I=120(e)^{0.25t}\nonumber\]
The number infected in 6 months is \(I=120(e)^{0.25(6)}\approx 538\).
Can you explain why the number infected was more with continuous growth than with periodic growth? It is similar to what happened with compounded interest where we gained interest on previous interest in the continuous model.
Interpret the following: \(S(t)=20e^{0.12t}\) if \(S(t)\) represents the growth of a substance in grams, and time is measured in days.
Solution
An initial substance weighing 20g is growing at a continuous rate of 12% per day.
Find the effective annual rate of an account which pays an 8% APR compounded continuously.
Solution
We can interpret the effective annual rate from the growth factor \(b = e^{r} = e^{0.08} \approx 1.08329\). After one year, the account will be 108.329% of the original amount. Therefore the effective annual rate is 8.329%.
Alternatively, after one year the account will have a value of \(A = ae^{(0.08)(1)} \approx a(1.08329) \) if an initial value of \(a\) is invested. Thus, the amount in one year will be 108.329% of the original amount. Therefore the effective annual rate is 8.329%.
A person ingests 20 mg of a medication.
a) If the amount of medication in a person's body decreases by 16% per hour, find a formula for the amount of medication, A, in the body after t hours. Then predict the amount of medication after 5 hours.
b) If the amount of medication in a person's body decreases continuously by 16%, find a formula for the amount of medication, A, in the body after t hours. Then predict the amount of medication after 5 hours.
- Answer
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a) In this scenario, we are given the periodic decay rate r = -16% = -0.16. Therefore, we should use the periodic exponential formula \(A=ab^{t}\), where a = 20 and b = 100% - 16% = 84% as a percent or b = 0.84 as a decimal. So the amount of medication is given by
\[A=120(0.86)^{t}\nonumber\]
The amount of medication in 5 hours is \(A=20(0.86)^{5}\approx 9.41\) mg.
b) In this scenario, we are given the continuous decay rate r = -16% = 0.16. Therefore, we should use the continuous exponential growth formula \(A=ae^{rt}\), where a = 20. So the amount of medication is given by
\[A=20(e)^{-0.16t}\nonumber\]
The amount of medication in 5 hours is \(A=20(e)^{-0.16(5)}\approx 8.99\) mg.
Focus: Some issues with using exponential functions to make predictions
Case: Predict the input when the output is known.
In Example 3.3.1a, the amount in the account after t years was given by \(A=1000(1.06)^{t} \). How long until there is $5,000 in the account?
Solution
We are given A = 5,000. We want the time t. Substituting we have, \[\begin{array}{l} {5000=1000(1.06)^{t}} \\ {\dfrac{5000}{1000}=(1.06)^{t}} \\ {5=(1.06)^{t}} \end{array}\nonumber\]
How can we get the variable t out of the exponent? We need to develop more tools to solve this exponential equation and make predictions like this with exponential models.
Case: Modeling data with a continuous exponential function
Find a continuous exponential model, \(y=ae^{rt}\) that contains the points (0,4) and (2,12).
Solution
The initial value is a = 4. To find r, substitute in the other data point t = 2 and y = 12, so \[\begin{array}{l} {12=4(e)^{r(2)} } \\ {\dfrac{12}{3}=e^{2r} } \\ {4=e^{2r}} \end{array}\nonumber\]
We run into the same issue as example 5, we need to get the variable out of the exponent.
Important Topics of this Section
- Continuous Exponential Growth
- Compound Interest
- Effective Annual Rate


13: Reproductive System
After completing this section, you should know:
- the role of mitosis and meiosis in the production of gametes (sperm and ova)
- that gametes are haploid cells
- that fertilization forms a diploid zygote
- the major parts of the male reproductive system and their functions
- the route sperm travel along the male reproductive tract to reach the penis
- the structure of a sperm and the difference between sperm and semen
- the difference between infertility and impotence
- the main parts of the female reproductive system and their functions
- the ovarian cycle and the roles of FSH, LH, oestrogen and progesterone
- the oestrous cycle and the signs of heat in rodents, dogs, cats and cattle
- the process of fertilization and where it occurs in the female tract
- what a morula and a blastocyst are
- what the placenta is and its functions
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- 13.1: Reproductive System
- In biological terms sexual reproduction involves the union of gametes - the sperm and the ovum - produced by two parents. Each gamete is formed by meiosis. This means each contains only half the chromosomes of the body cells (haploid). Fertilization results in the joining of the male and female gametes to form a zygote which contains the full number of chromosomes (diploid).
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- 13.15: Fertilization
- In most fish and amphibians (frogs and toads) fertilization of the egg cells takes place outside the body. The female lays the eggs and then the male deposits his sperm on or at least near them. In reptiles and birds, eggs are fertilized inside the body when the male deposits the sperm inside the egg duct of the female. The egg is then surrounded by a resistant shell, “laid” by the female and the embryo completes its development inside the egg.


12.4: Need Step
As opposed to the speech to inform, the first main point must serve as the Need step . Here speakers will frame a need for their audience so that they can follow it up with a satisfying solution (i.e., the action they will propose later in this speech). Also referred to as the “problem step,” this main point involves explaining the why behind the proposed action.
Home In September of 2009, Simon Sinek , an author and speaker in business and leadership studies, gave a TEDx talk in the Seattle area, where he presented the idea of what he dubbed “The Golden Circle.” To explain this, Sinek used the following diagram:
Using this model, Sinek explained that the majority of persuasive messages that people see, read, or hear on a regular basis work from the outside inward. They start with the what , or the result, and then explain the how , which represents their method or product, but stop there, expecting people to buy into their idea, their services, or their products. The examples Sinek used in his speech included: “Here’s our newest model of SUV ( what ). It has dual airbags, great gas mileage, and looks sharp ( how ).” Sinek went on to explain that these messages fail because they come across as uninspiring. They do not tap into the decision-making center of the brain—the limbic system—because they fail to inspire or engage by explaining why people need to buy this product.
Sinek then went on to describe the model used by Apple , which uses a highly successful persuasive model because it works from the inside out. As a company, Apple’s messages clearly begin with an explanation of why they conduct business by communicating with the world that, in everything they do, they believe in challenging the status quo and thinking differently. Only after Apple finishes explaining the why do they state that they achieve this goal by creating products that are beautifully designed, easy to operate, and challenge the limits of technology ( how ). Apple’s message then ends with the what by showing its audiences the products they can expect to benefit their lives.
In motivating an audience to action, speakers must tap into their audience’s why by explaining to them that a genuine and relatable need exists. They can complete this task by addressing the Need step in four components:
- Show the audience that a need or a problem exists and that it can and will affect each and every member of the audience in some way.
- Explain to the audience why it exists by providing context and history behind the need or problem. In other words, explain where the need arose and perhaps why nothing has been done about it until now.
- Demonstrate to the audience that this problem needs to be solved or this need must be addressed immediately—that it will not simply disappear on its own if left alone.
- Overcome potential objections. Why might the audience not believe that this need or problem affects them personally?
Returning to the example speech from earlier, the breakdown could look as follows:
Need Step
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Texting and driving is an all too common occurrence on our roads today.
- Using mobile technology to stay socially connected to others is remarkably addictive, according to a study performed by Dr. David Greenfield, founder of the Center for Internet and Technology Addiction, when cell phone users compulsively check their devices it is in an effort to stimulate the brain’s pleasure centers.
- In this way, cell phone use can be compared to gambling or gaming addictions, making even the most moral person succumb to the temptation of glancing down at a recently received notification.
Note : This half of the Need step provides the audience with context and background, effectively setting up the problem. Additionally, it shows the audience that the problem will not go away.
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Texting and driving drastically reduces driver attentiveness and creates life-altering hazardous driving conditions.
- According to a recent study, the average person glances at their phone for 5 seconds to check a message, while the average texting-related crash occurs within only 3 seconds of driver distraction.
- According to the Virginia Tech Transportation Institute, texting while driving is six times more likely to cause an auto crash than driving when intoxicated.
Note : This half of the Need step relates the problem to the audience, while also demonstrating a severe and life-threatening need to address the problem immediately.


Chapter 15: Redefining Creative Labor – East Asian Comparisons
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People often fantasize about Hollywood’s workforce being composed of innovative people imbued with refined tastes and aesthetics. They are further imagined as being well paid and therefore able to enjoy a rosy bohemian or bourgeois lifestyle, as opposed to other industrial workers. This romantic vision of the hip Hollywood creative may be apocryphal, but few would deny that the industry has long prospered because it has been able to foster and harness the creative energies of its employees.
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15.1: Introduction
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Introduction to the goal of this chapter: to investigate the values and attitudes of workers in game-related companies in Asia, and how they diverge from the traditional Western model of creativity.
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15.2: Problematizing Creativity
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Problematizing the model of the "creative class", developed in the 1990s from analysis of American creatives. Considering how varying socio-political contexts of creative industries result in different conceptions of creativity.
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15.3: Subcontracting and Subcontracted Creativity
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Forming a framework for cultural labor in globalized creative industries that considers how such labor in developing countries is often subcontracted from and subordinated to these global industries.
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15.4: Three Major Production Regions in Asia
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A brief overview of the historical and modern status of the games industry of three regions of Asia—Southeast Asia, Korea, and China—in relation to the global games industry.
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15.5: Modes of Creative Labor
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Developing a framework for analyzing globalized labor in creative industries, including subcontracted labor, with two major axes: creative dependence and tolerance for creativity.
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15.6: Three Modes of Cultural Labor
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Analyzing the cultures of the game industries in the three major Asian production locales, to identify the dominant mode of cultural labor in each: progressive artists in Korea, skilled enthusiasts in Southeast Asia, and contented bourgeois in China.
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15.7: Conclusion – Creative Industries With or Without Creativity
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Summary of the ways in which creativity is a relative concept, with reasons from globalized economic hierarchies to internal national ideologies.
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15.8: Notes
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1.3: Major Health Concerns
Leading Causes of Death in the United States
Do you know what the top two leading causes of death are for Americans? Heart disease takes the number one spot, followed by cancer. As you can see by the graph below, cancer death rates have been steadily increasing throughout the years. What does this potentially mean for the future? Is cancer going to take over as the number one leading cause of death? It certainly appears to be headed in that direction.
The 10 Leading Causes of Death in the United States:
- Heart disease: 614,348
- Cancer: 591,699
- Chronic lower respiratory diseases: 147,101
- Accidents (unintentional injuries): 136,053
- Stroke (cerebrovascular diseases): 133,103
- Alzheimer’s disease: 93,541
- Diabetes: 76,488
- Influenza and Pneumonia: 55,227
- Nephritis, nephrotic syndrome and nephrosis: 48,146
- Intentional self-harm (suicide): 42,773
To keep pace with emerging public health challenges and to address the leading causes of death and disability, CDC initiated an effort called Winnable Battles to achieve measurable impact quickly. Winnable Battles are public health priorities with large-scale impact on health and known effective strategies to address them. By identifying priority strategies, defining clear targets and working closely with our public health partners, we are making significant progress in reducing health disparities and the overall health burden from these diseases and conditions.
Contributors and Attributions
Public domain content
- Leading Causes of Death. Authored by : Centers for Disease Control and Prevention. Located at : http://www.cdc.gov/nchs/fastats/deaths.htm . License : Public Domain: No Known Copyright
- Winnable Battles. Authored by : Centers for Disease Control and Prevention. Located at : http://www.cdc.gov/winnablebattles/ . License : Public Domain: No Known Copyright


17.3: A World Full of Troubles
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The United States has been constantly engaged in military operations of one type or another since the end of the Cold War. The seizure of Kuwait by Saddam Hussein’s Iraq in 1990 is an early example. The United States led an international coalition to liberate Kuwait soon afterwards in what was known as the Gulf War. Unlike the second US-Iraq war 12 years later in 2003, the Gulf War of 1991 was authorised by the United Nations Security Council. Another mission for American forces just after the Cold War ended was the humanitarian effort in Somalia. Warring factions there had disrupted the distribution of food, causing widespread hunger and the potential for a major famine. Under a United Nations mandate, a US-led coalition sought to bring relief and stability to Somalia. Fighting among the factions soon spiralled out of control and the aid mission collapsed as the United States and other nations withdrew troops from the chaos to prevent any more of their personnel being killed or wounded. Somalia had become the classic failed state, a land and a people without a functioning government. The United States, chastened by the Somalian experience, has since been hesitant to help in other such cases. It turned away from intervening in the 1994 genocide in Rwanda, as did other members of the international community. However, it has gradually returned to involvement in Africa via training and supporting the regional coalitions acting as peacekeepers in African Union and/or United Nations operations, especially those directed against militant Islamic terrorist groups like Boko Haram. Significant effort has also gone into humanitarian projects related to fighting international piracy off the Horn of Africa and combatting pandemics such as Ebola and HIV/AIDS.
Elsewhere, the nations freed by the collapse of the Soviet Union face continuing problems as Russia seeks to reclaim lost territory and protect the interests of ethnic Russian populations caught on what they see as the wrong side of new borders. Russia annexed Crimea from Ukraine in 2014 and has also intervened in parts of Georgia and Moldova. And Ukraine endures a Russian-supported rebellion in its disaffected eastern regions. Although the United States now rotates combat units through Northern and Eastern European nations, and is constructing a ballistic missile defence system on NATO’s eastern frontier, West Europeans have been content to be mostly worried observers, concerned about Russian behaviour but also concerned about their trade with Russia. There seems no strong appetite in Europe to rise to the Russian challenge in any way other than via economic sanctions and punitive diplomacy.
Closer to home, in Latin America, there are constant problems with poverty, drugs and corruption. Haiti, the region’s poorest country, has had US troops as frequent visitors – for instance, to help the government survive a coup attempt and to provide relief after a devastating earthquake. Columbia required substantial assistance to suppress a persistent insurgency, fed in part by narcotics traffic. Less visibly, the United States helps Mexico cope with wars among rival drug gangs that have cost thousands of lives and threaten the stability of the Mexican government. Several Central American nations suffer similarly. Through the Mexican border and the Caribbean flows a flood of migrants seeking to escape poverty and crime by heading north into the United States.
More than six decades after the 1953 truce that ended the Korean War, one of the first battles of the Cold War, the United States still keeps nearly 30,000 troops in South Korea to protect it from North Korea. American forces also keep Japan separated from its neighbours, several of whom have territorial disputes with Japan and outstanding grievances tied to Japan’s behaviour prior to and during the Second World War. The most significant of the neighbours is China, whose expansive designs in the South China Sea appear to threaten the interests of many Southeast Asian states as well as the right of free passage for shipping through one of the most travelled international shipping routes. The US Navy has stepped up its patrols in the region and other elements of the US military, primarily the Marine Corps, have begun rotating units to Australia in what some have called the ‘Pivot’, a US military rebalance towards to Asia.
This quick contextual sweep across the globe does not reflect the central concern the United States has when it looks out to the world. Since 9/11, when it was attacked by Al-Qaeda, its main military preoccupation has been in fighting transnational terrorism. This includes a 2001 invasion of Afghanistan, where the leaders of Al-Qaeda were being harboured by the Taliban regime. It also includes drone and other raids in Pakistan where some of the terrorist leadership had fled. Most notably, perhaps, it also includes an invasion of Iraq in 2003 to depose Saddam Hussein, supposedly to eliminate his efforts to develop and stockpile weapons of mass destruction. Both Afghan and Iraqi actions succeeded quickly in removing the offending regimes, but led to ongoing and costly counter-insurgency campaigns that have destabilised neighbouring countries. The so-called ‘Global War on Terror’ has ensured that the gaze of the United States remains cast widely, especially in those regions where terrorism is prevalent such as the Middle East and North Africa. This extends beyond traditional military means into areas of intelligence and cyber warfare.


11.1: Avoiding the "Field of Dreams" Approach
By the end of this section, you will be able to:
- Understand the importance of planning
- Understand the concepts of product and service innovation, and define and understand key business models
- Describe and be able to construct a value proposition for a new business idea (product or service)
In the 1989 film Field of Dreams , Kevin Costner plays an Iowa farmer who hears a voice that tells him, “If you build it, he will come.” Inspired by this vision, Costner’s character turns his cornfield into a baseball field (of dreams), and eventually the ghosts of deceased baseball players such as Shoeless Joe Jackson appear on the field as younger versions of themselves. The movie coined the popular axiom that “if you build it, they will come,” just as the players appeared after the field of dreams was built. Although it’s a fun saying for film buffs and sports fans, this approach is one you will want to avoid in entrepreneurship. In fact, the entrepreneurial graveyard is littered with ghosts of startups that never gained traction with customers, never to be heard from again. (Seventy-five percent of venture-backed startups fail, according to one recent study.) 1 Thus, you don’t want to blindly build a product and hope that customers will come. Juicero is one recent example of product that conducted little-to-no customer discovery before launch. A cold press juicer made by this San Francisco startup cost $699 at launch. The juicer squeezed packs of cut up fruits and vegetables, but customers found they could just as easily squeeze the juice out of the packs by hand and avoid the hefty price of the juicer.
Customer acquisition and customer retention are not easy processes by any means. You have to work to gain a customer and work even harder to get her to return. One study by the data analysis firm CBInsights of why 101 startups failed found that 42 percent of them joined the “entrepreneurial afterlife” because there was “no market need,” which suggests a customer (or lack thereof) problem. 2 Current trends in entrepreneurial thinking reflect a customer-centric approach: From the start, entrepreneurs infuse their insights into the planning process through a process called “customer discovery.” The entrepreneurial journey should begin with finding what the serial entrepreneur, author, and educator Steve Blank, one of the founders of modern entrepreneurship, calls the problem/solution fit. 3 , 4 In a complementary approach, the Mosaic/Netscape founder Marc Andreesen discussed the need to achieve product-market fit. 5 In other words, don’t just build a baseball field and expect players to show up. This is an oversimplification, but if we extend the Field of Dreams analogy before blindly believing in the magic, you would want to talk to prospective players and fans to see if a field is needed, what type of field (corn-to-baseball?), why that field is needed, how that field would be used, and what features of the field would be most useful— before you go to bat ( Figure 11.2 ). 6
Business Model
Although there are countless varieties of business models, the Scaling Lean author Ash Maurya offers three common types: direct, multisided, and marketplace. Direct businesses are the most common and involve one-sided actors—that is, users—becoming your customers. A coffee shop is a classic example; other examples include retail stores, software as a service (SaaS), many mobile apps, hardware stores, and stores that sell physical goods. In multisided models, users and customers—multi-actors—are usually different people. Ad-based models, big data, and enterprise are common examples where the products are free to users, and their value is monetized by a different customer base. Marketplace models are a more complex variant of multisided models made up of two different customer segments of buyers and sellers. eBay and Airbnb are well-known examples of marketplace models. 7
Although planning is important, adaptability within the planning process is equally important. That’s what the business model approach is all about: outlining an approach but changing that approach throughout if or when you discover that your assumptions and educated guesses were wrong. For each new iteration, or version, the entrepreneur makes a minor change to the current business model to better capitalize on market opportunities.
Successful entrepreneurs are often multidimensional: part dreamer, part pragmatist. Adam Grant, Wharton School of Business professor and author of the best-selling book Origins: How Non-Conformists Move the World , explores how entrepreneurs are “capable of recognizing a good idea, speaking up without getting silenced, building a coalition of allies, choosing the right time to act, and managing fear and doubt.” 8 Entrepreneur magazine tells the story of FedEx founder Fred Smith, who, while attending Yale University in the mid-1960s, wrote an economics term paper on the need for a new approach to overnight delivery in the computer age. His professor, unimpressed with Smith’s idea, graded his paper a C because the idea was not feasible. 9 After graduation, using innovative thinking, dogged determination, and hard work, Smith would turn his “unfeasible” concept into the world's first overnight delivery company, and in so doing, change the transportation industry forever. Smith embodied the entrepreneurial concept of being part dreamer, part pragmatist.
Read about the popular corporate narratives related to relatively new companies. Consider whether these stories involve inventor-founders. If so, what is the invention and how does that tie in with the current and future narrative of the company?
Listen to the NPR podcast “How I Built This” with Guy Raz to hear stories about more than 100 startup companies and their founders.
Several more brief narratives on how to tell your company’s story are also available.
Sports metaphors offer important entrepreneurial lessons beyond insights on customer discovery and planning. In baseball and softball, you must field a team to enter the game. In boxing, you enter the ring alone to go toe to toe with your competitor (where some of the best-laid plans get thrown out after you get hit). The tides of entrepreneurial thinking have shifted from the twentieth-century economist Joseph Schumpeter’s early belief that it is “lone individuals who carry novelty” for wider market exploitation and benefit to society to the notion that it takes a team to innovate and back to the idea that individuals can enact entrepreneurial change. 10 “Solopreneurs,” for instance, are hard-working entrepreneurs who are comfortable working alone on all the requisite tasks of starting a venture. 11 At the same time, many successful investors preach the merits of teams in entrepreneurship. Venture capitalist Aileen Lee says that people are the second-most important factor behind addressable market when evaluating startups. 12 The cohesion, diversity, and makeup of the team all contribute to investable worthiness and potential entrepreneurial success ( Figure 11.3 ). Many successful accelerator programs have typically required teams in order to be considered for entry into their programs. The accelerator Techstars has said that what they look for in a startup is “team, team and team,” 13 and the accelerator Boomtown requires at least two present founders for the duration of its accelerator program. 14
Multiple shifts in sources of innovations and rapid business model exploration may reflect high startup failure rates. Lack of planning is also a major reason for failure. Most small businesses fail within the first few years because of cash-flow issues. With more people today willing to field a startup team or enter the entrepreneurial ring, failure is more often than not a part of the entrepreneurial journey. Serial entrepreneurs launch numerous ventures, many of which fail, before moving on to other efforts. Entrepreneurs are the modern-day equivalent of Hamilton: An American Musical ’s Hercules Mulligan to the world: They get back up again after getting knocked down.
Innovation
One of the fundamental theories of entrepreneurship is that it brings innovation , which can be a new addition to the market or a novel change to an existing product or service. The famed management guru Peter Drucker put it simply: “Entrepreneurs innovate.” 15 Of course, we should note that not all entrepreneurial ventures involve innovation. Even for those that do, however, the term innovation can be ambiguous. Further complicating the issue, a plethora of different extensions (or “types”) has arisen surrounding the concept of innovations—such as radical, incremental, and disruptive—that have been used to describe and emphasize different innovations in different situations. 16 Innovation can also refer to products or processes because there are differences between product innovation and process innovation. In other words, not all innovations are created equal. 17
As it pertains to entrepreneurship, the creative destruction of old markets with inferior technology and the creation of new markets, as defined by Schumpeter back in the 1930s, occurs through disruptive innovation . 18
The adjective disruptive also became a bit of a catchphrase in the 1990s during the first Internet era, largely due to the popularity of Clayton Christensen’s Figure 11.4 theory of incumbent failure in the face of what he first termed “disruptive technology” and later renamed “disruptive innovation.” 19
As Christensen defines them, disruptive innovations are often more advantageous to new entrants than to incumbent firms. This is because once market uncertainty occurs as a consequence of the disruption around the disruptive product, established firms consider it irrational to abandon their existing paying customers for the smaller customer base of the new, initially small market for what they believe is inferior technology. New entrants challenge incumbent firms by either creating markets where no markets exist, turning nonconsumers into consumers, or by targeting overlooked segments of the market and later moving up market as the product improves. Leading firms’ decision criteria for developing new products and commercializing innovations are all biased toward supporting incremental innovations that build on their existing technology base and help maintain or grow revenue and profitability in established markets. This opens the door for startups to develop and introduce disruptive innovations and profit from them. Table 11.1 lists some disruptive innovations.
| Area | Timeframe | Established Market | Disruptive Innovation |
|---|---|---|---|
| Medical imaging | 1960s | X-rays | Ultrasound offered a new type of imaging; X-ray companies lost out to the market and could not match the innovation, although eventually they purchased many ultrasound companies |
| Screens | 1990s–2000s | CRT (cathode ray tube) | LED/LCDs innovated to overcome their display limitations, replacing heavy and bulky CRTs. More recent innovations like foldable screens and retinal scans have added more functionality and “intelligence” to link to Internet of Things devices |
| Entertainment | 2000s | Video rental | Streaming services ousted much of the video rental market and companies like Blockbuster found themselves irrelevant in the market. More recently, multiple streaming services along with proprietary content (and “Over the Top” menu options) have disrupted cable TV companies |
Netflix’s Disruption
Netflix, founded in 1997 in California, disrupted video rental stores such as Blockbuster with its subscription service, which mailed DVDs directly to customers’ homes. The rental stores, whose business model was predicated on revenue from late fees, could not compete with the ease and convenience of home delivery coupled with lower costs than the per-tape rental fees. But as streaming video content directly to televisions or over-the-top devices disrupted Netflix’s original DVD-by-mail model, Netflix moved to offer a streaming service in addition to the DVD by mail model. In both instances, Netflix’s prevailing model was predicated on serving as a distribution outlet for content created by other businesses. Netflix in recent years has begun not only distributing others’ content but creating its own TV and movie content as well. ( Orange Is the New Black and The Unbreakable Kimmy Schmidt are both original Netflix series; The Irishman is an original Netflix film.) Now content creators such as Disney and Marvel are creating their own streaming distribution platforms to exclusively deliver their own content, eventually pulling those shows from Netflix.
- What should Netflix do to counter this threat to the third iteration of its business model?
- What threats does the end of net neutrality pose to Netflix’s business model?
- If you were in charge at Netflix, would you pay more to Internet providers to gain faster delivery of your content on the Internet? Why or why not?
In separate but related work, Christensen also developed the jobs-to-be-done theory, which aids companies in determining how to create products and services that customers want to buy by getting at the causal driver behind a purchase. Christensen uses the term job as shorthand for what an individual wants to accomplish in a given circumstance, often with social, emotional, and functional dimensions. For example, two jobs that a newspaper does for its readers are to inform and entertain, whereas the jobs to be done of a newspaper are completely different for another customer segment—advertisers. A newspaper’s jobs to be done for advertisers, for instance, may include promotions, attracting customers, or selling products. The jobs-to-be-done approach has also been incorporated into the development of business models in the form of customer empathy maps and value proposition canvases covered. 20
Watch this video illustrating Christensen’s jobs-to-be-done theory through a milkshake to learn more.
After you watch this video, think about how Christensen’s definition of jobs relates to innovation. What are some jobs to be done for your entrepreneurial idea?
Disruptive innovations are contrasted with sustaining technologies, which improve the performance of established products through characteristics that mainstream customers adopt. Disruptive technologies allow for new entrants in the market, often with simpler, more affordable, more convenient products. Entrepreneurs and marketers have difficulty predicting or projecting how the emergence of an innovation will occur, and anticipating how customers will react to the new offerings. Predicting who the early adopters will be can also be difficult during the early stage of an innovation’s emergence. The mainstream customer base initially fails to find value in the new product. New customer segments, however, see value in the new features and lower prices. Eventually, developments improve the new product’s features to a level that will satisfy mainstream customers and thus attract more of the mainstream market. 21
Ride Sharing
Ride-sharing services disrupted the traditional taxicab business by providing a mobile platform that connected ride-seeking consumers with drivers willing to provide transportation. In rapidly becoming the market leader of ride-sharing services, Uber became the poster child for disruptive innovation. A customer using a ride-sharing service like Uber or Lyft no longer had to wave down a cab on the street, nor did she need cash in hand anymore through its mobile payment system within the app. An Uber ride usually costs less than a regular cab ride. Ride-sharing services also offer more versatility in choices and greater overall convenience. Now Uber continues to evolve its model, adding options like Uber Eats and Uber Copter.
- What are the jobs to be done that Uber addresses?
- What areas of a taxi cab’s business model does Uber disrupt?
Christensen prefers the term disruptive innovation to disruptive technology because even in his original theoretical framework, technology was not the driving force disrupting existing markets, products, and models—rather, business models were. 22 The root of the tension in disruptive innovation is the conflict between the previously established business model for the incumbent technology and the new business model that may be necessary for exploiting the disruptive technology or process.
The efforts of incumbents to capitalize on a disruptive technology will fail in most instances because commercializing the new technology will require a different business model from the one that the incumbents currently use. When disruption occurs, incumbents struggle to commercialize, whereas new entrants take control through their mastery of the requisite new business models. Thus, a disruptive business model can fundamentally reshape profits within an industry because managers are faced with a technological disruption/innovation that alters their businesses, specifically their business models. This phenomenon is known as business model innovation. 23
Business model innovation , as defined by Professor Constantinos Markides of the London Business School, occurs when an existing business fundamentally changes their business model. 24 In order to be an innovation, the “new business model must enlarge the existing economic pie, either by attracting new customers or by encouraging existing consumers to consume more.” Disruptive innovations tend to require a business model that is not only different from but even in conflict with the traditional way of competing. 25 In contrast, radical innovations (see the preceding text) are new-to-the-world products that are disruptive to both consumers and producers.
In the context of disruptive innovation, business model innovation is distinct from open business model innovation, which leverages external ideas together with internal ones. We also can define a business model innovation as a reformulation of an existing product or service, including a shift in how it is provided to the end user. A business model innovation “leads to a new way of playing the game” and can consist of new performance attributes on price or distribution outlets. 26 Stitch Fix uses data to offer personal styling at scale and ships customized clothing boxes from its own in-house label and from 1,000 brands in its collection directly to customers who want to avoid the hassles of in-store shopping. Despite volatility from investors, which dropped its initial $5.1 billion valuation at offering by two-thirds over three months, the company continues to reinvent the $334 billion US apparel industry. 27
Value Proposition
Entrepreneurs play a key role in determining the value of their products. Of course, there are financial measures of value such as economic performance, job creation, wealth, and growth measures. But more often than not, value creation at the outset of a new startup venture lies outside these financial realms and addresses instead individual value to customers. The value proposition in a business model, for example, is a summary describing the benefits (value) customers can expect from a particular product or service. Your value proposition describes the benefits customers can expect from your products and services. 28 The value proposition is an integral part of the business model canvas, which we will discuss in Designing the Business Model .
From Odeo to Twitter
Evan Williams and Biz Stone, both ex-Google employees, began a podcasting platform startup called Odeo around 2005. According to an early engineer in the company, Blaine Cooke, they built and tested Odeo but never used it. Shortly after co-founder Noah Glass created Odeo’s podcasting platform, Apple announced plans to include a podcasting platform in all of its iPods. Faced with the reality that many of Odeo’s fourteen employees weren’t using the product they had built and the emergence of a giant competitor with a tremendous unfair advantage in Apple, Williams decided Odeo’s future wouldn’t be in podcasting.
The company held hackathons among employees and began searching for a pivot. One of those fourteen Odeo employees, Jack Dorsey, focused his efforts on the problem of status, the position of affairs at a particular time. In February 2006, Dorsey, Glass, and Florian Weber, a German contract developer, presented what they called Twttr, a system whereby a user could send a text message to a phone number, and it would be broadcast to the user’s friends. A month later, Odeo had a working Twttr prototype, while obsessed employees were racking up hundreds of dollars in text messaging bills using the product. By the fall, Twitter (as it was now called) had thousands of users. Many began to see the product’s utility after a San Francisco earthquake when it was heavily used to broadcast messages throughout the Bay Area.
- What type of innovation would you consider the original Odeo platform? Why?
- Why did Apple have an “unfair advantage” with its podcasting platform over competitors like Odeo?
- What value proposition did the early version of Twttr offer its users?


4.2: The Dynamic Process
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- Jennifer Paris, Kristin Beeve, & Clint Springer
- College of the Canyons
Curriculum planning for young children is a dynamic process that takes into account children’s ideas and interests. As stated earlier, infant/toddler and preschool curriculum should reflect the unique context of each group of children, families, and teachers. The curriculum plan that works well for one group of children may generate little interest in another group of children. [1]
For Example:
A group of children living near a large urban park may have the opportunity to experience several trips to check on a nest with eggs laid by one of the ducks living at the pond nearby. The ducks, their habitat, and the eggs become the object of study for several weeks, as the children discuss, tell stories, plan ways to protect the eggs from danger, and count the days of waiting. The teachers did not anticipate this curriculum prior to the discovery of the duck nest, yet the duck nest became part of their curriculum plans . Another group of three- and four-year-olds in a different program in the same city might be developing the same emerging skills and learning the same concepts yet be focused on their classroom pet—a tree frog—exploring his food likes and discovering how to maintain his habitat in a way that keeps him healthy and thriving. Like most journeys, early childhood curriculum follows a course that is unique for each group of children, with unpredictable content from group to group and from setting to setting . [2]
What is constant and predictable in a dynamically generated curriculum is the foundation of concepts and skills that teachers support as children pursue ideas and topics of interest. Through professional preparation, teachers who work with young children understand how to recognize the concepts and skills described in California’s early learning foundations. Teachers look for opportunities to engage the minds of young children in meaningful play, interaction, conversation, and investigation—creating curriculum that nurtures the inquisitive minds of the children and connects with their experiences and developing knowledge and skills. Dynamic curriculum emerges throughout the year and changes each year as teachers respond to the unique teaching opportunities that present themselves. [3]
Co-Constructed Curriculum
Early childhood curriculum is co-constructed with input from family members, teachers, and the children themselves. Teachers and families observe and reflect together on children’s experiences and generate many possible ideas for what new experiences or materials might extend and render more complex and coherent children’s thoughts, feelings, and ideas. In volume 2 of the California Preschool Curriculum Framework (CDE 2011b), the story of children’s investigation of fresh food from the garden illustrates the dynamic and co-constructed nature of early childhood curriculum. In this excerpt from a vignette in volume 2 (CDE 2011b, 17), the teachers describe how they generate possibilities for exploring this topic with a group of three- and four-year-olds: [4]
Vignettes
In this project, both parents and teachers wanted to find ways to support children’s health and nutrition, a desire that emerged during a presentation at a parent meeting on nutrition and obesity prevention in young children. Many of the parents were surprised to learn that “picky eating” is a stage that can evolve into long-term resistance to eating fruits and vegetables and that one way to prevent children from becoming resistant is to encourage them to try a variety of fresh produce.
An idea that emerged from the discussion was to give children a series of opportunities to explore and taste fresh fruits, vegetables, and other edible plants in their natural, preprocessed state. Parents and teachers together began to think about the varied smells, textures, colors, and tastes of locally grown fruits, vegetables, and edible plants that young children could explore.
In this particular vignette, the teachers and families co-construct an idea for a curriculum project. In other situations, an idea that becomes the topic for an ongoing investigation might come from a child. When an idea for a curriculum project is proposed, teachers generate possibilities for how that idea might be explored, being mindful of how, within the investigation or project, children might have an opportunity to use emerging foundational skills and concepts. The teachers invite families to join them in coming up with ideas for the investigation. In the investigation of fresh foods from the garden, the following planning question guided discussions among teachers and families: How might we give children an opportunity to explore and learn about fresh fruits and vegetables grown in the garden?
Reflecting on different possibilities, the teachers became curious to see what children would do if given the chance to explore root crops such as carrots, beets, or onions that still had stems and leaves attached. Teachers shared this idea with children’s families through a note near the sign-in sheet. Soon after the note was posted, one of the parents brought in big bunches of fresh mint that she was ready to remove from an overgrown section of her yard. Other families responded to the note by offering to bring in cucumbers, apples, and lemons from local gardens or farmers markets. Teachers began to anticipate the ways in which children might build emerging skills, concepts, and ideas in exploring these plants.
In the preceding example, teachers are aware of how this topic holds possibilities for children’s learning to extend to multiple domains of study. Children will have opportunity to use foundational concepts in mathematics and science, story comprehension and language, as well as skills in drawing and painting, among others. Teachers will also look forward to sharing and naming for families their children’s learning, as the investigation directly connects with key concepts and skills children are acquiring in each of the domains of learning. [5]
Responsive Approach
Early childhood curriculum planning is responsive to the interests and opportunities that exist in a group of children, families, and community. This means that as they plan, teachers observe and listen to children’s ideas. Curriculum plans that are dynamic, collaboratively constructed with children, and responsive put children’s thinking at the center of the curriculum planning process. Teachers should be reflecting on what is meaningful to the children within their community. Rinaldi (2006a) offers this advice on how to approach curriculum planning that is responsive to children’s thinking: “What kind of context, what kind of possibility can you offer to the children for the next step and the next step, not because you know the next step, but because you want to offer [them] a possibility for going deeper and deeper in their research?”
A written plan that is responsive is seen as holding “possibilities” for children’s inquiry, rather than delivered as an activity focused solely on a particular skill. A responsive plan may be proposed as a question—“What might happen if we . . .?” or, “In what ways will the children explore . . .?” When posed as a question, the plan prompts teachers to observe what ensues and to record what delights, surprises, amazes, or puzzles the children. Mindfully noting children’s responses adds to teachers’ understanding of how children are thinking and making sense of the experience. A responsive plan is more than simply the proposed activity written on a planning form. It includes observations of what occurs and teachers’ interpretations of what children appear to be thinking and feeling during the experience. The following table illustrates how teachers might create a plan that offers possibilities for children to explore, along with examples of observations and interpretations of how children engage with the materials. The interpretations will inform what might come next in the curriculum as well as inform the ongoing assessment of children’s learning. [6]
|
Plan of Possibilities [7] |
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Planning Question: “What will happen when the toddlers encounter squeeze bottles in the play spaces?” |
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Observation: |
Photos Taken |
Interpretation: |
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Jerrod wrapped his fingers around the bottle, but no liquid emerged. Elaine makes a steady stream of water emerge from her squeeze bottle. She looks at Jerod, frowning and whining, and then reaches over and squeezes Jerrod’s bottle for him. He smiles, but then pushes her hand away and tries squeezing the bottle again. Alexander and Raj find the squeeze bottles in the play kitchen and squeeze imaginary liquid into pots on the stove. Raj directs Alexander: “Like this! Put some in the soup.” |
X |
This was a struggle for J., because he still grasps and holds things with his full hand. [DRDP (CDE 2015) Fine Motor]. We may want to adapt the object using a bottle that is easier to squeeze (i.e., easier to grasp and hold), so that he can experience success. E. interacts in simple ways with familiar peers as they play side by side. [DRDP (CDE 2015) Social and Emotional Understanding] She wants to help J in a simple way. A. & J. incorporate this simple tool into their pretend play [DRDP (CDE 2015) Symbolic Play.] Adding plastic squeeze bottles that are easier to squeeze will also offer an element of discovery for the others, who might begin to experiment with the pressure they need to exert in order to make the water flow. |
DRDP refers to the Desired Results Developmental Profile (CDE 2015), a periodic assessment of an infant’s learning. The Plan of Possibilities was adapted and used with permission (Maguire-Fong 2015).
It is the careful observation and documentation of what children do and say as they play that generates ideas for the next steps in the investigation. The next step might simply be to change or add materials, as a way of extending or adding complexity to the play and to offer children opportunities to build and to use emerging concepts and skills. Teachers look for moments in which the children are amazed or surprised. Documentation of what children found unexpected not only provides evidence of their sense of wonder about what people and things are like and the way things work, but it also guides what to plan next in the curriculum. [8]
References
[1] The Integrated Nature of Learning by the California Department of Education is used with permission
[2] The Integrated Nature of Learning by the California Department of Education is used with permission
[3] The Integrated Nature of Learning by the California Department of Education is used with permission
[4] The Integrated Nature of Learning by the California Department of Education is used with permission
[5] The Integrated Nature of Learning by the California Department of Education is used with permission
[6] The Integrated Nature of Learning by the California Department of Education is used with permission; Content by Clint Springer is licensed under CC BY 4.0
[7] The Integrated Nature of Learning by the California Department of Education is used with permission
[8] The Integrated Nature of Learning by the California Department of Education is used with permission


10.3: Nutrition and Chronic Hematologic Illness
By the end of this section, you should be able to:
- 10.2.1 Discuss the impact of nutrition on congenital hematologic disorders.
- 10.2.2 Discuss the impact of nutrition on cancers.
Congenital Hematologic Disorders
Sickle cell disease (SCD) , a genetic hemoglobinopathy with chronic anemia, is the most common inherited blood disorder in the United States (McCaskill et al., 2018) and affects the shape of hemoglobin, resulting in blocked blood flow. Individuals with SCD are more prone to micronutrient and macronutrient (carbohydrate, fat, and protein) deficiencies related to hyperreactive hematopoiesis , the physiologic response caused by chronic anemia. Nutrient deficiencies (Table 10.5) further increase systemic oxidative stress (disturbance in the balance between the production of free radicals and antioxidant defenses) and contribute to severe and frequent sickle cell vaso-occlusive crises . These deficiencies can cause the following in people with SCD (Umeakunne & Hibbert, 2019):
- Delayed growth and development
- Decreased quality of life
- Chronic inflammation
- Painful vaso-occlusive crises
- Increased occurrence of stroke, pulmonary hypertension, heart disease, and renal disease
As with SCD, thalassemia is a genetic hemoglobinopathy, characterized by less oxygen-carrying protein and fewer red bloods cells. There are multiple genetic forms ranging in severity. Thalassemia carries the same nutritional risks as SCD does.
Table 10.5 outlines additional micronutrient deficiencies and recommended interventions.
| Micronutrient Deficiency | Recommended Foods/Interventions |
|---|---|
| Vitamin D* | Milk, yogurt, cheese |
| Vitamin A | Carrots, sweet potatoes, kale, spinach |
| Vitamin C | Kiwis, oranges |
| Vitamin E | Mustard greens, sunflower seeds |
| Zinc | Nuts, fish, whole grains, dairy products |
| Folic acid |
1 mg daily supplement
Leafy green vegetables |
| Vitamin B 12 | Steamed shrimp, baked snapper, whole grain breads |
| Omega-3 fatty acids | Meats, beans, nuts, seeds, vegetable oils |
| *Vitamin D deficiency is five times more likely to occur in children with SCD than in children without SCD and is associated with increased hospitalizations (McCaskill et al, 2018). |
Genetic Hemochromatosis
Genetic hemochromatosis causes excessive absorption of dietary iron secondary to decreased expression of the peptide hormone hepcidin. It is the most common autosomal recessive disorder in White individuals, affecting one in 300–500 people of northern European descent (Porter & Prashanth, 2023). It is twice as common in males as females and can result in multiple organ dysfunction. Excessive intestinal dietary intake of heme and nonheme iron is primarily managed by dietary modifications (Milman, 2021). These modifications are extensive and require nutritional counseling and reinforcement by health care professionals:
- Consider a vegetarian or semivegetarian diet.
- Consume 21 oz of fruit and vegetables daily; fresh is best.
- Avoid red meat from mammals; instead, choose lean, white poultry.
- Avoid processed meat. Consume no more than 7 oz of meat from poultry per week. Consider additional protein sources such as fish, eggs, and legumes.
- Choose whole grains; avoid iron-enriched grains.
- Beverages should consist of water, green or black tea, coffee, and low-fat milk. Avoid alcoholic beverages.
Hemophilia
Hemophilia is an inherited X-linked blood disorder resulting in decreased levels of clotting factor VIII or IX. Occurring in 1 in 5,000 male births, this deficiency results in spontaneous bleeding , often in joints , and severe bleeding following injury or trauma (CDC, 2023a). Nutritional considerations include managing weight and maintaining iron levels to avoid IDA. Obesity is common secondary to a sedentary lifestyle to avoid injury-induced bleeding ; however, consequences of decreased physical activity include more stress on the joints and muscle strains that can result in musculoskeletal bleeding (Lim et al., 2020). A recommended diet includes iron-rich foods such as lean red meat, leafy green vegetables, broccoli, dried beans, grains, and raisins. It is important to consume foods containing vitamin C, such as orange juice, to enhance iron absorption.
The American Society of Hematology (2009) offers a video that demonstrates how blood flow is affected by misshapen red blood cells.
Impact of Cancer on Nutrition and Hematologic Function
Advanced age is a risk factor for nutritional deficiency; the addition of chronic diseases, including malignancy, can quickly lead to malnourishment. These comorbidities can contribute to reduced tolerance of anticancer therapy , impacting survival (Stauder et al., 2020).
The prevalence of anemia in cancer can exceed 90% across all ages and is generally considered to be related to medications, infections, or disorders of hematopoiesis. Common concerns are alterations in activities of daily living affecting quality of life, decreased productivity, and inability to work. Fatigue is reported as the most common troubling symptom of cancer and is directly linked to anemia (Gilreath & Rodgers, 2020). Fatigue and lack of appetite commonly coexist, resulting in an inability to prepare meals, further exacerbating anemia.
Anemia was traditionally believed to be primarily related to the adverse effects of anticancer therapy; however, recent research has shown a direct correlation with chronic, low-grade inflammation. Functional iron deficiency (state in which iron is insufficiently incorporated into erythroid precursors even though body iron stores are apparently adequate), malnutrition, and anorexia contribute to cancer-associated anemia (Natalucci et al., 2021). See Table 10.6 for types of IDA in cancer. In contrast, iron overload can occur in clients with symptomatic anemia receiving red blood cell transfusions and can alter the function of effective hematopoiesis, contributing to anemia (Gilreath & Rodgers, 2020). Other micronutrient deficiencies affecting hematologic function in individuals with cancer include folate and vitamin B 12 .
Approximately 50% of adults with colon cancer have anemia due to chronic blood loss from the gastrointestinal tract (Chardalias et al., 2023). The prevalence of anemia in other cancers ranges from 29–46%, mainly related to chronic disease, chemotherapy-induced anemia, nutrient-related anemia, chronic anorexia , and gastrointestinal adverse effects such as nausea, vomiting, and diarrhea (Busti et.al., 2018).
| Iron Deficiency | Etiology |
|---|---|
| Absolute iron deficiency anemia | Associated with bleeding; total body iron stores diminish. |
| Iron sequestration * | Inflammation results in iron being unavailable for erythropoiesis . |
| Iron-restricted erythropoiesis * | Erythropoiesis therapy (epoetin) outpaces iron delivery from storage. |
| *Functional iron deficiency anemia |
Nutritional Interventions
Chronic illness has a significant impact on nutrition and, consequently, hematologic wellness. Recommendations have evolved due to more emphasis on a holistic approach to caring for those with hemoglobinopathies and cancer.
The Mediterranean diet has gained popularity in the United States as a way to manage weight, lower cholesterol, and stabilize blood sugar. Close investigation of the constituents of this eating lifestyle reveals significant anti-inflammatory properties that translate well to chronic hematologic illness. Extra-virgin olive oil is has been found to block the proinflammatory cascade (Natalucci et al., 2021).
The following foods and substances rich in antioxidants contribute to anti-inflammatory and microbiota-modulating properties:
- Phytochemical vitamins in red, orange, and yellow fruits and dark green leafy vegetables
- Ginger
- Green tea
- Garlic
- Black pepper
- Turmeric
To avoid severe nutritional deficiencies, a high-calorie, nutrient-rich diet is essential for people living with SCD and thalassemia . Increased oral hydration is vital in SCD to decrease the frequency of painful vaso-occlusive events. Additional recommendations include daily supplements of omega-3 fatty acids, folic acid, high-dose vitamin D, and a multivitamin without iron. For clients with thalassemia specifically, drinking black tea may decrease the gastrointestinal absorption of iron (Goldberg et al., 2018; Physicians Committee for Responsible Medicine, 2020b; Srichairatanakool et al., 2020).
People with SCD and vitamin D deficiency consuming a diet rich in fish, milk, cheese, and eggs were found to have decreased hospital and emergency department visits (McCaskill et al., 2018). High-dose vitamin D replacement (greater than 3000 units per day) has been found to augment immune response and decrease the risk of respiratory infections in SCD (Umeakunne & Hibbert, 2019). Recent literature strongly correlates that vitamin D and chronic inflammation play an important role in regulating iron homeostasis, which can improve anemia (Natalucci et al., 2021).
Adults living with hemoglobinopathies should avoid drinking alcohol because it potentiates the oxidative damage caused by iron overload (Milman, 2021).


1.22: Book XXII
THE KILLING OF THE SUITORS—THE MAIDS WHO HAVE MISCONDUCTED THEMSELVES ARE MADE TO CLEANSE THE CLOISTERS AND ARE THEN HANGED.
 He shed the arrows on to the ground at his feet and said, “The mighty contest is at an end. I will now see whether Apollo will vouchsafe it to me to hit another mark which no man has yet hit.”
On this he aimed a deadly arrow at Antinous, who was about to take up a two-handled gold cup to drink his wine and already had it in his hands. He had no thought of death—who amongst all the revellers would think that one man, however brave, would stand alone among so many and kill him? The arrow struck Antinous in the throat, and the point went clean through his neck, so that he fell over and the cup dropped from his hand, while a thick stream of blood gushed from his nostrils. He kicked the table from him and upset the things on it, so that the bread and roasted meats were all soiled as they fell over on to the ground. 166 The suitors were in an uproar when they saw that a man had been hit; they sprang in dismay one and all of them from their seats and looked everywhere towards the walls, but there was neither shield nor spear, and they rebuked Ulysses very angrily.
Thus they spoke, for they thought that he had killed Antinous by mistake, and did not perceive that death was hanging over the head of every one of them. But Ulysses glared at them and said:
“Dogs, did you think that I should not come back from Troy?  You have feared neither God nor man, and now you shall die.”
They turned pale with fear as he spoke, and every man looked round about to see whither he might fly for safety, but Eurymachus alone spoke.
“If you are Ulysses,” said he, “then what you have said is just. We have done much wrong on your lands and in your house.  It was all his doing. It was not that he wanted to marry Penelope; he did not so much care about that; what he wanted was something quite different, and Jove has not vouchsafed it to him; he wanted to kill your son and to be chief man in Ithaca.  We will make everything good among ourselves, and pay you in full for all that we have eaten and drunk. Each one of us shall pay you a fine worth twenty oxen, and we will keep on giving you gold and bronze till your heart is softened. Until we have done this no one can complain of your being enraged against us.”
Ulysses again glared at him and said, “Though you should give me all that you have in the world both now and all that you ever shall have, I will not stay my hand till I have paid all of you in full. You must fight, or fly for your lives; and fly, not a man of you shall.”
Their hearts sank as they heard him, but Eurymachus again spoke saying:
“My friends, this man will give us no quarter.  Let us then show fight; draw your swords, and hold up the tables to shield you from his arrows.
As he spoke he drew his keen blade of bronze, sharpened on both sides, and with a loud cry sprang towards Ulysses, but Ulysses instantly shot an arrow into his breast that caught him by the nipple and fixed itself in his liver. He dropped his sword and fell doubled up over his table. The cup and all the meats went over on to the ground as he smote the earth with his forehead in the agonies of death, and he kicked the stool with his feet until his eyes were closed in darkness.
Then Amphinomus drew his sword and made straight at Ulysses to try and get him away from the door; but Telemachus was too quick for him, and struck him from behind; the spear caught him between the shoulders and went right through his chest, so that he fell heavily to the ground and struck the earth with his forehead.   I will arm myself as well, and will bring other armour for the swineherd and the stockman, for we had better be armed.”
“Run and fetch them,” answered Ulysses, “while my arrows hold out, or when I am alone they may get me away from the door.”
Telemachus did as his father said, and went off to the store room where the armour was kept. He chose four shields, eight spears, and four brass helmets with horse-hair plumes. He brought them with all speed to his father, and armed himself first, while the stockman and the swineherd also put on their armour, and took their places near Ulysses. Meanwhile Ulysses, as long as his arrows lasted, had been shooting the suitors one by one, and they fell thick on one another: when his arrows gave out, he set the bow to stand against the end wall of the house by the door post, and hung a shield four hides thick about his shoulders; on his comely head he set his helmet, well wrought with a crest of horse-hair that nodded menacingly above it, 168 and he grasped two redoubtable bronze-shod spears.
Now there was a trap door 169 on the wall, while at one end of the pavement 170 there was an exit leading to a narrow passage, and this exit was closed by a well-made door. Ulysses told Philoetius to stand by this door and guard it, for only one person could attack it at a time. But Agelaus shouted out, “Cannot some one go up to the trap door and tell the people what is going on? Help would come at once, and we should soon make an end of this man and his shooting.”
“This may not be, Agelaus,” answered Melanthius, “the mouth of the narrow passage is dangerously near the entrance to the outer court. One brave man could prevent any number from getting in. But I know what I will do, I will bring you arms from the store-room, for I am sure it is there that Ulysses and his son have put them.”
On this the goatherd Melanthius went by back passages to the store-room of Ulysses’ house. There he chose twelve shields, with as many helmets and spears, and brought them back as fast as he could to give them to the suitors. Ulysses’ heart began to fail him when he saw the suitors 171 putting on their armour and brandishing their spears. He saw the greatness of the danger, and said to Telemachus, “Some one of the women inside is helping the suitors against us, or it may be Melanthius.”
Telemachus answered, “The fault, father, is mine, and mine only; I left the store room door open, and they have kept a sharper look out than I have. Go, Eumaeus, put the door to, and see whether it is one of the women who is doing this, or whether, as I suspect, it is Melanthius the son of Dolius.”
Thus did they converse. Meanwhile Melanthius was again going to the store room to fetch more armour, but the swineherd saw him and said to Ulysses who was beside him, “Ulysses, noble son of Laertes, it is that scoundrel Melanthius, just as we suspected, who is going to the store room. Say, shall I kill him, if I can get the better of him, or shall I bring him here that you may take your own revenge for all the many wrongs that he has done in your house?”
Ulysses answered, “Telemachus and I will hold these suitors in check, no matter what they do; go back both of you and bind Melanthius’ hands and feet behind him. Throw him into the store room and make the door fast behind you; then fasten a noose about his body, and string him close up to the rafters from a high bearing-post, 172 that he may linger on in an agony.”
Thus did he speak, and they did even as he had said; they went to the store room, which they entered before Melanthius saw them, for he was busy searching for arms in the innermost part of the room, so the two took their stand on either side of the door and waited. By and by Melanthius came out with a helmet in one hand, and an old dry-rotted shield in the other, which had been borne by Laertes when he was young, but which had been long since thrown aside, and the straps had become unsewn; on this the two seized him, dragged him back by the hair, and threw him struggling to the ground. They bent his hands and feet well behind his back, and bound them tight with a painful bond as Ulysses had told them; then they fastened a noose about his body and strung him up from a high pillar till he was close up to the rafters, and over him did you then vaunt, O swineherd Eumaeus saying, “Melanthius, you will pass the night on a soft bed as you deserve. You will know very well when morning comes from the streams of Oceanus, and it is time for you to be driving in your goats for the suitors to feast on.”
There, then, they left him in very cruel bondage, and having put on their armour they closed the door behind them and went back to take their places by the side of Ulysses; whereon the four men stood in the cloister, fierce and full of fury; nevertheless, those who were in the body of the court were still both brave and many. Then Jove’s daughter Minerva came up to them, having assumed the voice and form of Mentor. Ulysses was glad when he saw her and said, “Mentor, lend me your help, and forget not your old comrade, nor the many good turns he has done you. Besides, you are my age-mate.”
But all the time he felt sure it was Minerva, and the suitors from the other side raised an uproar when they saw her. Agelaus was the first to reproach her. “Mentor,” he cried, “do not let Ulysses beguile you into siding with him and fighting the suitors.
This made Minerva still more furious, so she scolded Ulysses very angrily. 173 “Ulysses,” said she, “your strength and prowess are no longer what they were when you fought for nine long years among the Trojans about the noble lady Helen. You killed many a man in those days, and it was through your stratagem that Priam’s city was taken.
But she would not give him full victory as yet, for she wished still further to prove his own prowess and that of his brave son, so she flew up to one of the rafters in the roof of the cloister and sat upon it in the form of a swallow.
Meanwhile Agelaus son of Damastor, Eurynomus, Amphimedon, Demoptolemus, Pisander, and Polybus son of Polyctor bore the brunt of the fight upon the suitors’ side; of all those who were still fighting for their lives they were by far the most valiant, for the others had already fallen under the arrows of Ulysses.  They are standing at the doors unsupported. Do not aim at him all at once, but six of you throw your spears first, and see if you cannot cover yourselves with glory by killing him. When he has fallen we need not be uneasy about the others.”
They threw their spears as he bade them, but Minerva made them all of no effect. One hit the door post; another went against the door; the pointed shaft of another struck the wall; and as soon as they had avoided all the spears of the suitors Ulysses said to his own men, “My friends, I should say we too had better let drive into the middle of them, or they will crown all the harm they have done us by killing us outright.”
  These all bit the dust, and as the others drew back into a corner Ulysses and his men rushed forward and regained their spears by drawing them from the bodies of the dead.
The suitors now aimed a second time, but again Minerva made their weapons for the most part without effect. One hit a bearing-post of the cloister; another went against the door; while the pointed shaft of another struck the wall. Still, Amphimedon just took a piece of the top skin from off Telemachus’s wrist, and Ctesippus managed to graze Eumaeus’s shoulder above his shield; but the spear went on and fell to the ground. Then Ulysses and his men let drive into the crowd of suitors. Ulysses hit Eurydamas, Telemachus Amphimedon, and Eumaeus Polybus. After this the stockman hit Ctesippus in the breast, and taunted him saying, “Foul-mouthed son of Polytherses, do not be so foolish as to talk wickedly another time, but let heaven direct your speech, for the gods are far stronger than men. I make you a present of this advice to repay you for the foot which you gave Ulysses when he was begging about in his own house.”
 Then Minerva from her seat on the rafter held up her deadly aegis, and the hearts of the suitors quailed. They fled to the other end of the court like a herd of cattle maddened by the gadfly in early summer when the days are at their longest. As eagle-beaked, crook-taloned vultures from the mountains swoop down on the smaller birds that cower in flocks upon the ground, and kill them, for they cannot either fight or fly, and lookers on enjoy the sport—even so did Ulysses and his men fall upon the suitors and smite them on every side.
Leiodes then caught the knees of Ulysses and said, “Ulysses I beseech you have mercy upon me and spare me. I never wronged any of the women in your house either in word or deed, and I tried to stop the others. I saw them, but they would not listen, and now they are paying for their folly.
Ulysses looked sternly at him and answered, “If you were their sacrificing priest, you must have prayed many a time that it might be long before I got home again, and that you might marry my wife and have children by her. Therefore you shall die.”
With these words he picked up the sword that Agelaus had dropped when he was being killed, and which was lying upon the ground.
The minstrel Phemius son of Terpes—he who had been forced by the suitors to sing to them—now tried to save his life. He was standing near towards the trap door, 174 and held his lyre in his hand. He did not know whether to fly out of the cloister and sit down by the altar of Jove that was in the outer court, and on which both Laertes and Ulysses had offered up the thigh bones of many an ox, or whether to go straight up to Ulysses and embrace his knees, but in the end he deemed it best to embrace Ulysses’ knees. So he laid his lyre on the ground between the mixing bowl 175 and the silver-studded seat; then going up to Ulysses he caught hold of his knees and said, “Ulysses, I beseech you have mercy on me and spare me. You will be sorry for it afterwards if you kill a bard who can sing both for gods and men as I can. I make all my lays myself, and heaven visits me with every kind of inspiration. I would sing to you as though you were a god, do not therefore be in such a hurry to cut my head off. Your own son Telemachus will tell you that I did not want to frequent your house and sing to the suitors after their meals, but they were too many and too strong for me, so they made me.”
Telemachus heard him, and at once went up to his father. “Hold!” he cried, “the man is guiltless, do him no hurt; and we will spare Medon too, who was always good to me when I was a boy, unless Philoetius or Eumaeus has already killed him, or he has fallen in your way when you were raging about the court.”
Medon caught these words of Telemachus, for he was crouching under a seat beneath which he had hidden by covering himself up with a freshly flayed heifer’s hide, so he threw off the hide, went up to Telemachus, and laid hold of his knees.

Ulysses smiled at him and answered, “Fear not; Telemachus has saved your life, that you may know in future, and tell other people, how greatly better good deeds prosper than evil ones. Go, therefore, outside the cloisters into the outer court, and be out of the way of the slaughter—you and the bard—while I finish my work here inside.”
The pair went into the outer court as fast as they could, and sat down by Jove’s great altar, looking fearfully round, and still expecting that they would be killed. Then Ulysses searched the whole court carefully over, to see if anyone had managed to hide himself and was still living, but he found them all lying in the dust and weltering in their blood. They were like fishes which fishermen have netted out of the sea, and thrown upon the beach to lie gasping for water till the heat of the sun makes an end of them. Even so were the suitors lying all huddled up one against the other.
Then Ulysses said to Telemachus, “Call nurse Euryclea; I have something to say to her.”
Telemachus went and knocked at the door of the women’s room. “Make haste,” said he, “you old woman who have been set over all the other women in the house. Come outside; my father wishes to speak to you.”
When Euryclea heard this she unfastened the door of the women’s room and came out, following Telemachus.  When she saw all the corpses and such a quantity of blood, she was beginning to cry out for joy, for she saw that a great deed had been done; but Ulysses checked her, “Old woman,” said he, “rejoice in silence; restrain yourself, and do not make any noise about it; it is an unholy thing to vaunt over dead men. Heaven’s doom and their own evil deeds have brought these men to destruction, for they respected no man in the whole world, neither rich nor poor, who came near them, and they have come to a bad end as a punishment for their wickedness and folly. Now, however, tell me which of the women in the house have misconducted themselves, and who are innocent.” 176
“I will tell you the truth, my son,” answered Euryclea. “There are fifty women in the house whom we teach to do things, such as carding wool, and all kinds of household work. Of these, twelve in all 177 have misbehaved, and have been wanting in respect to me, and also to Penelope. They showed no disrespect to Telemachus, for he has only lately grown and his mother never permitted him to give orders to the female servants; but let me go upstairs and tell your wife all that has happened, for some god has been sending her to sleep.”
“Do not wake her yet,” answered Ulysses, “but tell the women who have misconducted themselves to come to me.”
 “Begin,” said he, “to remove the dead, and make the women help you. Then, get sponges and clean water to swill down the tables and seats. When you have thoroughly cleansed the whole cloisters, take the women into the space between the domed room and the wall of the outer court, and run them through with your swords till they are quite dead, and have forgotten all about love and the way in which they used to lie in secret with the suitors.”
On this the women came down in a body, weeping and wailing bitterly. First they carried the dead bodies out, and propped them up against one another in the gatehouse. Ulysses ordered them about and made them do their work quickly, so they had to carry the bodies out. When they had done this, they cleaned all the tables and seats with sponges and water, while Telemachus and the two others shovelled up the blood and dirt from the ground, and the women carried it all away and put it out of doors. Then when they had made the whole place quite clean and orderly, they took the women out and hemmed them in the narrow space between the wall of the domed room and that of the yard, so that they could not get away: and Telemachus said to the other two, “I shall not let these women die a clean death, for they were insolent to me and my mother, and used to sleep with the suitors.”
So saying he made a ship’s cable fast to one of the bearing-posts that supported the roof of the domed room, and secured it all around the building, at a good height, lest any of the women’s feet should touch the ground; and as thrushes or doves beat against a net that has been set for them in a thicket just as they were getting to their nest, and a terrible fate awaits them, even so did the women have to put their heads in nooses one after the other and die most miserably. 178 Their feet moved convulsively for a while, but not for very long.
As for Melanthius, they took him through the cloister into the inner court.
When they had done this they washed their hands and feet and went back into the house, for all was now over; and Ulysses said to the dear old nurse Euryclea, “Bring me sulphur, which cleanses all pollution, and fetch fire also that I may burn it, and purify the cloisters. Go, moreover, and tell Penelope to come here with her attendants, and also all the maidservants that are in the house.”
“All that you have said is true,” answered Euryclea, “but let me bring you some clean clothes—a shirt and cloak. Do not keep these rags on your back any longer. It is not right.”
“First light me a fire,” replied Ulysses.
She brought the fire and sulphur, as he had bidden her, and Ulysses thoroughly purified the cloisters and both the inner and outer courts.  It made him feel as if he should like to weep, for he remembered every one of them. 179