4.3 Exponential Decay

<
>
• 7. Saber-Toothed Cat

The half-life of a snake's venom is the amount of time it takes for 50% of the venom to be removed from an animal's body.

A snake bit a saber-toothed cat, injecting 20 milligrams of venom into its blood. The venom had a half-life of 40 hours. Assume the saber-toothed cat was still alive after 80 hours. How much of the venom remained in its bloodstream? (See Example 3 and Example 4.)

• Worked-Out Solution

Use the formula for half-life.

After 80 hours, there is still 5 milligrams of the venom left in the cat's bloodstream.

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.

``` ______      ___      _  __   __   __
|      \\   / _ \\   | |/ //  \ \\/ //   ____
|  --  //  / //\ \\  | ' //    \ ` //   |    \\
|  --  \\ |  ___  || | . \\     | ||    | [] ||
|______// |_||  |_|| |_|\_\\    |_||    |  __//
`------`  `-`   `-`  `-` --`    `-`'    |_|`-`
`-`
```
• 8. Tasmanian Tiger

The half-life of a snake's venom is the amount of time it takes for 50% of the venom to be removed from an animal's body. A snake bit a Tasmanian tiger, injecting 40 milligrams of venom into its blood. The venom had a half-life of 16 hours. Assume the Tasmanian tiger was still alive after 2 days. How much of the venom remained in its bloodstream? (See Example 3 and Example 4.)

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.

```  ______    ______             _    _    _    _
/_   _//  /_   _//   ____    | || | || | \  / ||
| ||     -| ||-   |    \\  | || | || |  \/  ||
_| ||     _| ||_   | [] ||  | \\_/ || | .  . ||
/__//     /_____//  |  __//   \____//  |_|\/|_||
`--`      `-----`   |_|`-`     `---`   `-`  `-`
`-`
```
• 9. Snake Venom

The half-life of a snake's venom is the amount of time it takes for 50% of the venom to be removed from an animal's body.

A snake bit a saber-toothed cat, injecting 20 milligrams of venom into its blood. The venom had a half-life of 40 hours. A snake bit a Tasmanian tiger, injecting 40 milligrams of venom into its blood. The venom had a half-life of 16 hours. How long did it take the amount of venom in each animal's bloodstream to drop to 10 milligrams? ( See Example 3 and Example 4.)

• Worked-Out Solution

Enter the following formulas into a spreadsheet.

Saber-toothed cat

Tasmanian tiger

For the saber-toothed cat, it takes about 40 hours for the amount of venom to drop to 10 milligrams.

For the Tasmanian tiger, it takes about 32 hours for the amount of venom to drop to 10 milligrams.

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.

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

```
• 10. Carbon Dating

The venom eventually killed the saber-toothed cat. An archaeologist discovers the remains and calculates that the ratio of carbon-14 to carbon-12 is about one-eighth of that occurring in the atmosphere. How long ago did the saber-toothed cat live? (See Example 3 and Example 4.)

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.

``` _    _     _____                ___      _  __
| \  / ||  |  ___||     ___     / _ \\   | |/ //
|  \/  ||  | ||__      /   ||  / //\ \\  | ' //
| .  . ||  | ||__     | [] || |  ___  || | . \\
|_|\/|_||  |_____||    \__ || |_||  |_|| |_|\_\\
`-`  `-`   `-----`      -|_|| `-`   `-`  `-` --`
`-`
```
• 11. Carbon Dating

The venom eventually killed the Tasmanian tiger. An archaeologist discovers the remains and calculates that the Tasmanian tiger lived 500 years ago. Estimate the ratio of carbon-14 to carbon-12 in the remains. (See Example 3 and Example 4.)

• Worked-Out Solution

For a time of 500 years, the ratio of carbon-14 to carbon-12 in the remains is given by

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.

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

```
• 12. Snake Venom

A snake bit a saber-toothed cat, injecting 20 milligrams of venom into its blood. Suppose the half-life of the venom injected into the saber-toothed cat was 20 hours. Would this increase or decrease the answer to Exercise 7? Explain. (See Example 3 and Example 4.)

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.
```  ______    _____     _  __     ___      ______