### Chapter 7 Review Exercises

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• 9. Flour Beetle Population Growth

The graph shows the growth of a flour beetle population in a natural environment. At what rate is the flour beetle population increasing?

• Worked-Out Solution

By making a spreadsheet of the data, you can see that the consecutive ratios are equal. This implies that the pattern is exponential. Moreover, the population is doubling every week.

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

```
• 10. Flour Beetle Population Growth

The graph shows the growth of a flour beetle population in a natural environment. Predict the number of flour beetles in week 6.

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```  ____       ___      ______     ___     ______
|  _ \\    / _ \\   /_____//   / _ \\  |      \\
| |_| ||  / //\ \\  `____ `   / //\ \\ |  --  //
| .  //  |  ___  || /___//   |  ___  |||  --  \\
|_|\_\\  |_||  |_|| `__ `    |_||  |_|||______//
`-` --`  `-`   `-`  /_//     `-`   `-` `------`
`-`
```
• 11. Flour Beetle Population Growth

The graph shows the growth of a flour beetle population in a natural environment. When does the population exceed 4000 beetles?

• Worked-Out Solution

From the spreadsheet below, you can see that if the population continues to double every week, then the population of flour beetles will exceed 4000 in the 10th week.

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``` _____       ___      ______     ___     _    _
|  __ \\    / _ \\   /_____//   / _ \\  | || | ||
| |  \ ||  / //\ \\  `____ `   / //\ \\ | || | ||
| |__/ || |  ___  || /___//   |  ___  ||| \\_/ ||
|_____//  |_||  |_|| `__ `    |_||  |_|| \____//
-----`   `-`   `-`  /_//     `-`   `-`   `---`
`-`
```
• 12. Flour Beetle Population Growth

The graph shows the growth of a flour beetle population in a natural environment. How many weeks does it take the population to quadruple?

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```            _____     _____     _____    __   __
___    |  ___||  |__  //   |  ___||  \ \\/ //
/   ||  | ||__      / //    | ||__     \   //
| [] ||  | ||__     / //__   | ||__     / . \\
\__ ||  |_____||  /_____||  |_____||  /_//\_\\
-|_||  `-----`   `-----`   `-----`   `-`  --`
`-`
```
• 13. Growth Pattern

In a laboratory, the growth of a flour beetle population in a container of flour is monitored for 12 weeks. The graph shows the growth of the population. What type of growth does the graph display?

• Worked-Out Solution

The graph is showing a logistic growth pattern.

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``` __   _    _    _    __   __    _____
| || | || | || | ||  \ \\/ //  |  ___||     ___
| '--' || | || | ||   \   //   | ||__      /   ||
| .--. || | \\_/ ||   / . \\   | ||__     | [] ||
|_|| |_||  \____//   /_//\_\\  |_____||    \__ ||
`-`  `-`    `---`    `-`  --`  `-----`      -|_||
`-`
```
• 14. Maximum Sustainable Population

In a laboratory, the growth of a flour beetle population in a container of flour is monitored for 12 weeks. The graph shows the growth of the population. What is the maximum sustainable population?

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``` _    _    __   __    ____       ___      _  _
| \  / ||  \ \\/ //  |  _ \\    / _ \\   | \| ||
|  \/  ||   \ ` //   | |_| ||  | / \ ||  |  ' ||
| .  . ||    | ||    | .  //   | \_/ ||  | .  ||
|_|\/|_||    |_||    |_|\_\\    \___//   |_|\_||
`-`  `-`     `-`'    `-` --`    `---`    `-` -`

```
• 15. Change in Population

In a laboratory, the growth of a flour beetle population in a container of flour is monitored for 12 weeks. The graph shows the growth of the population. Make a table that shows the change in the number of flour beetles for each week. Discuss any trends.

• Worked-Out Solution

Enter the data into a spreadsheet. Then, add a column that shows the weekly change. Notice that the change is increasing until Week 4. At that point, the growth rate starts to slow down.

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```  ______     ___                 ___     ______
/_____//   / _ \\      ___     / _ \\  |      \\
`____ `   | / \ ||    /   ||  | / \ || |  --  //
/___//    | \_/ ||   | [] ||  | \_/ || |  --  \\
`__ `      \___//     \__ ||   \___//  |______//
/_//       `---`       -|_||   `---`   `------`
`-`                     `-`
```
• 16. Percent Change in Population

In a laboratory, the growth of a flour beetle population in a container of flour is monitored for 12 weeks. The graph shows the growth of the population. Make a table that shows the percent change in the number of flour beetles for each week. Discuss any trends.

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```  ____     __   __   _    _      ___      _____