### 4.1 Exponential Growth

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• 7. Swine Flu Pandemic

A pandemic is an outbreak of infectious disease or condition that spreads through a large part of the human population. There have been numerous pandemics throughout history such as smallpox and tuberculosis. Current pandemics include HIV and certain strains of influenza. Once a pandemic reaches Phase 6, the number of infected people can grow exponentially.

From June 2009 through August 2010, the swine flu (H1N1) was considered a pandemic by the World Health Organization. Ten people in a community are infected with the swine flu. The next day, 26 people are infected. The growth rate is 160% per day. At this rate, how many people will be infected in 1 week? Graph the results. (See Example 3 and Example 4.)

• Worked-Out Solution

The formula for this exponential growth is

The number of people who will be infected in 1 week is

You can use a spreadsheet to graph the pandemic.

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```  ______   __   __               ___     _    _
/_____//  \ \\/ //   ____      / _ \\  | \  / ||
`____ `    \ ` //   |    \\   / //\ \\ |  \/  ||
/___//      | ||    | [] ||  |  ___  ||| .  . ||
`__ `       |_||    |  __//  |_||  |_|||_|\/|_||
/_//        `-`'    |_|`-`   `-`   `-` `-`  `-`
`-`                 `-`
```
• 8. Exponential Growth of Pandemic

Use the rate in Exercise 7 to find the number of people who will be infected after 1 week when the initial number of people infected is 50. (See Example 3 and Example 4.)

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```  _____     _____    _____      _____    _____
/  ___||  |  ___|| |  __ \\   |  ___|| |  __ \\
| // __    | ||__   | |  \ ||  | ||__   | |  \ ||
| \\_\ ||  | ||__   | |__/ ||  | ||__   | |__/ ||
\____//   |_____|| |_____//   |_____|| |_____//
`---`    `-----`   -----`    `-----`   -----`

```
• 9. 1918-1920 Pandemic

The 1918-1920 flu pandemic, commonly known as the Spanish flu, killed about 40 million people worldwide. That is more than twice the number of lives claimed by World War I. Estimates for the growth rate vary. Suppose 2 people are infected and the number of infected people triples every 3 days. How many people will be infected in 21 days? Graph the results. (See Example 3 and Example 4.)

• Worked-Out Solution

The formula for this exponential growth is

Notice that if the number triples each day, this is a growth rate of 200%.

The number of people who will be infected in 21 days is

You can use a spreadsheet to graph the pandemic.

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```  _  __     ___      ____       ___
| |/ //   / _ \\   |  _ \\    / _ \\      ___
| ' //   | / \ ||  | |_| ||  / //\ \\    /   ||
| . \\   | \_/ ||  | .  //  |  ___  ||  | [] ||
|_|\_\\   \___//   |_|\_\\  |_||  |_||   \__ ||
`-` --`   `---`    `-` --`  `-`   `-`     -|_||
`-`
```
• 10. 1918-1920 Pandemic

Use the rate in Exercise 9. How many people will be infected in 42 days? (See Example 3 and Example 4.)

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``` __   _      ___      _____     _____
| || | ||   / _ \\   /  ___||  |  ___||     ___
| '--' ||  / //\ \\ | // __    | ||__      /   ||
| .--. || |  ___  ||| \\_\ ||  | ||__     | [] ||
|_|| |_|| |_||  |_|| \____//   |_____||    \__ ||
`-`  `-`  `-`   `-`   `---`    `-----`      -|_||
`-`
```
• 11. Exponential Graph

Describe the graph of an exponential growth model. (See Example 3 and Example 4.)

• Worked-Out Solution

The graph of the exponential model is a curve that rises more and more rapidly as n increases.

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```  ______     ___     __   __    ______    _____
/_   _//   / _ \\   \ \\/ //  /_   _//  / ____||
`-| |,-   | / \ ||   \   //    -| ||-  / //---`'
| ||    | \_/ ||   / . \\    _| ||_  \ \\___
|_||     \___//   /_//\_\\  /_____//  \_____||
`-`'     `---`    `-`  --`  `-----`    `----`

```
• 12. Growth Rate

Many factors affect the spread of a disease. Describe some factors that would influence the growth rate of an infectious disease. Would these factors increase or decrease the growth rate?

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```  _____     _____   __    __   __   __