### 7.2 Exponential Patterns

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• 15. Trout Population

A lake is stocked with 200 trout. The graph shows the growth of the trout population. What is the maximum sustainable population? Explain your reasoning. (See Example 5.)

• Worked-Out Solution

From the graph, the maximum sustainable population appears to be around 4000 trout.

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

```
• 16. Trout Population Growth

A lake is stocked with 200 trout. The graph shows the growth of the trout population. Make a table that shows the change in the number of trout for each year. Discuss any trends. (See Example 5.)

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``` __   __     ___      ______   _    _     _  __
\ \\/ //   / _ \\   /_____// | || | ||  | |/ //
\   //   / //\ \\  `____ `  | || | ||  | ' //
/ . \\  |  ___  || /___//   | \\_/ ||  | . \\
/_//\_\\ |_||  |_|| `__ `     \____//   |_|\_\\
`-`  --` `-`   `-`  /_//       `---`    `-` --`
`-`
```
• 17. Changes in Trout Population

A lake is stocked with 200 trout. The graph shows the growth of the trout population. Make a table that shows the percent change in the number of trout for each year. Discuss any trends. (See Example 5.)

• Worked-Out Solution

Begin by entering the data into a spreadsheet. Then, find the percent change each year.

The percent of increase is decreasing each year. Eventually, the percent increase will approach 0 and the population will stabilize.

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

```
• 18. Comparing Growth Patterns

A lake is stocked with 200 trout. The graph shows the growth of the trout population. Make a table comparing the number of trout for each year in the graph to the number of trout each year if the trout population grew exponentially by 60% each year. Why is exponential growth unrealistic in this situation? (See Example 5.)

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```             ___       _____   _    _     _____
____      / _ \\    / ___// | || | ||  / ____||
|    \\   | / \ ||   \___ \\ | || | || / //---`'
| [] ||   | \_/ ||   /    // | \\_/ || \ \\___
|  __//    \___//   /____//   \____//   \_____||
|_|`-`     `---`   `-----`     `---`     `----`
`-`
```
• 19. Competing Species

The graphs show the growth of the populations of two competing species of fish when they are released into separate ponds and when they are released into the same pond. Assume all the ponds are the same size and have the same resources. Compare the growth of the populations of the two species when they are released into separate ponds. (See Example 6.)

• Worked-Out Solution

When released into separate ponds, both species of fish experience a logistic growth pattern.

Species A levels off with a population of about 1400 fish.

Species B levels off with a population of about 1000 fish.

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

```
• 20. Competing Species

The graphs show the growth of the populations of two competing species of fish when they are released into separate ponds and when they are released into the same pond. Assume all the ponds are the same size and have the same resources. Compare the growth of the populations of the two species when they are released into the same pond. (See Example 6.)

These comments are not screened before publication. Constructive debate about the information on this page is welcome, but personal attacks are not. Please do not post comments that are commercial in nature or that violate copyright. Comments that we regard as obscene, defamatory, or intended to incite violence will be removed. If you find a comment offensive, you may flag it.

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

```
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