### Chapter 4 Review Exercises

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• 15. Medicine

Subjects in a study receive daily doses of a medicine for 10 weeks. In the first week, they receive 100 milligrams each day. Each week thereafter, the dosage decreases 10% from the previous week. Write a formula that represents the daily dosage during each week.

• Worked-Out Solution

The formula for this exponential decay is

P = 100 people, r = 10%, n is the number of weeks

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

```
• 16. Making a Table to Show Medicine Dosage

Subjects in a study receive daily dose of a medicine for 10 weeks. In the first week, they receive 100 milligrams each day. Each week thereafter, the dosage decreases 10% from the previous week. Make a table showing the daily dosage during the 10 weeks.

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```__    __   __   __               ___      ______
\ \\ / //  \ \\/ //   ____      / _ \\   /_   _//
\ \/ //    \ ` //   |    \\   | / \ ||    | ||
\  //      | ||    | [] ||   | \_/ ||   _| ||
\//       |_||    |  __//    \___//   /__//
`        `-`'    |_|`-`     `---`    `--`
`-`
```
• 17. Graphing the Decrease of Medicine Dosage

Subjects in a study receive daily doses of a medicine for 10 weeks. In the first week, they receive 100 milligrams each day. Each week thereafter, the dosage decreases 10% from the previous week. Sketch a graph showing the decrease in the daily dosage during the 10 weeks.

• Worked-Out Solution

The formula for this exponential decay is

P = 100 people, r = 10%, n is the number of weeks

Use a spreadsheet to graph the dosage for the 10 weeks.

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

```
• 18. Half-life of Medicine

Subjects in a study receive daily doses of a medicine for 10 weeks. In the first week, they receive 100 milligrams each day. Each week thereafter, the dosage decreases 10% from the previous week. The half-life of the medicine is 24 hours. How much of the medicine received in a dose during week 10 remains in the patient's bloodstream after 24 hours?

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

```
• 19. Technetium

Most technetium is man-made in nuclear reactors. There are many isotopes of technetium, two of which are technetium-99 and technetium-99m. The half-life of technetium-99 is 210,000 years. How much of a 120-gram sample of technetium-99 will remain after 630,000 years?

• Worked-Out Solution

After 210,000 years,

remain. After another 210,000 years

remain. After another 210,000 years

remain. So, after 630,000 years, 15 grams remain.

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```           __   __    _____      ___     __   _
___    \ \\/ //  /  ___||   / _ \\  | || | ||
/   ||   \ ` //  | // __    / //\ \\ | '--' ||
| [] ||    | ||   | \\_\ || |  ___  ||| .--. ||
\__ ||    |_||    \____//  |_||  |_|||_|| |_||
-|_||    `-`'     `---`   `-`   `-` `-`  `-`
`-`
```
• 20. Decay of Technetium

Most technetium is man-made in nuclear reactors. There are many isotopes of technetium, two of which are technetium-99 and technetium-99m. The half-life of technetium-99 is 210,000 years. A vial contains 10 grams of technetium-99m. Use the spreadsheet to determine how long it will take the 10 grams of technetium-99m to decay to about 2.1 grams

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``` __   __   __   __   _    _     ______
\ \\/ //  \ \\/ // | \  / ||  /_   _//     ___
\   //    \ ` //  |  \/  ||   -| ||-     /   ||
/ . \\     | ||   | .  . ||   _| ||_    | [] ||
/_//\_\\    |_||   |_|\/|_||  /_____//    \__ ||
`-`  --`    `-`'   `-`  `-`   `-----`      -|_||
`-`
```
• 21. Half-life of Technetium

A vial contains 10 grams of technetium-99m. The table shows the amount remaining after various periods of time.

What is the half-life of technetium-99m? Explain your reasoning.

• Worked-Out Solution

From the table, you can see that it took 6 years for the amount to decay from 10 grams to 5 grams.

This implies that the half-life is 6 years.

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

```
• 22. Storing Technetium

Most technetium is man-made in nuclear reactors. There are many isotopes of technetium, two of which are technetium-99 and technetium-99m. The half-life of technetium-99 is 210,000 years. A solution containing technetium-99m is often injected into a patient to help diagnose problems in the body. Explain why a hospital or veterinary clinic should not order excessive amounts of technetium-99m with the intent of placing it in storage.

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```  ____      _____               _____    _    _