### 4.3 Exponential Decay

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• Math Help

In Example 1, note that n represents the number of turbines and not elapsed time. The relationship between the numbers of turbines and salmon, however, can be modeled by the formula for exponential decay. Also, be sure you understand that the numbers of survivors are rounded down. The numbers are rounded down because it is not reasonable to count "half of a fish" as a survivor. So, when n = 3, you should find the amount as shown.

For a further discussion on the rounding of numbers, see Section 1.2.

To make a spreadsheet for Example 1, use the steps below. [Note that Step 6 uses the exponential decay formula given in Example 1, ]

1. Enter the titles "Turbines, n" and "Survivors" into row 1.
2. Enter 0 into cell A2.
3. Enter the formula =A2 + 1 into cell A3.
4. Select cell A3. From the Edit menu, choose Copy.
5. Select cells A4 through A8. From the Edit menu, choose Paste.
6. Enter the formula =ROUNDDOWN(100000*0.85^A2, 0) into cell B2.
7. Select cell B2. From the Edit menu, choose Copy.
8. Select cells B3 through B8. From the Edit menu, choose Paste.
9. Select cells B2 through B8. From the Format menu, choose Cellsâ€¦.
10. In the Format Cells dialog, select the Number tab.
11. From the Category: list, select Number.
12. For Decimal places:, enter 0. Check the Use 1000 Separator (,) box. Then click OK.

• Consumer Suggestion

Hydroelectric dams are an example of a renewable energy source. A renewable energy source can be replenished either by humans or nature. Other renewable energy sources are:

• Solar energy
• Wind energy
• Geothermal energy
• Biomass energy

Renewable energy sources allow us to depend less on the limited supply of fossil fuels, such as coal, petroleum, and gas, to create energy.

For more information on both renewable and nonrenewable energy, ways to save energy, and current energy statistics, visit the Energy Information Administration.

• Checkpoint Solution

Use the formula for exponential decay.

Because there can't be a fraction of a salmon left, 14,224 salmon will survive.

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

```