### 4.3 Exponential Decay

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• Math Help

Here are some additional algebraic steps for finding the exponential decay rate in Example 6.

So, r = 0.25. Note that in the context of the problem in Example 6, r = 0.25 corresponds to an exponential decay rate of 25% every 10,000 years.

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• Checkpoint Solution

It took the plutonium 80,000 years to decay to its original size (from 10 grams to 1 gram).

Because it is decaying at a constant exponential rate, it will take 80,000 more years to decay to its size again (from 1 gram to gram).

You can check this result using the formula for exponential decay

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

```