You are taking an 800-mg dose of an antibiotic every 8 hours. Your body eliminates 50% of the drug in 8 hours. How much of the drug will be in your system after three doses?

Algebra and Trigonometry (6th Edition)
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ISBN:9780134463216
Author:Robert F. Blitzer
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Question 39:**
You are taking an 800-mg dose of an antibiotic every 8 hours. Your body eliminates 50% of the drug in 8 hours. How much of the drug will be in your system after three doses?

**Explanation:**

This question involves calculating the remaining amount of a drug in the system after multiple doses, taking into account the body's elimination rate.

1. **Initial Dose (First Dose):**
   - Dose: 800 mg
   - After 8 hours, the body eliminates 50% of the drug.
   - Remaining drug after 8 hours: 800 mg * 0.5 = 400 mg

2. **Second Dose:**
   - New dose after 8 hours: 800 mg
   - Total drug amount in the system right after the second dose: 400 mg (remaining from first dose) + 800 mg = 1200 mg
   - After the next 8 hours, the body eliminates 50% of the drug.
   - Remaining drug after 8 hours: 1200 mg * 0.5 = 600 mg

3. **Third Dose:**
   - New dose after another 8 hours: 800 mg
   - Total drug amount in the system right after the third dose: 600 mg (remaining from second dose) + 800 mg = 1400 mg
   - After the next 8 hours, the body eliminates 50% of the drug.
   - Remaining drug after 8 hours: 1400 mg * 0.5 = 700 mg

So, after three doses, there will be **700 mg** of the drug in your system.
Transcribed Image Text:**Question 39:** You are taking an 800-mg dose of an antibiotic every 8 hours. Your body eliminates 50% of the drug in 8 hours. How much of the drug will be in your system after three doses? **Explanation:** This question involves calculating the remaining amount of a drug in the system after multiple doses, taking into account the body's elimination rate. 1. **Initial Dose (First Dose):** - Dose: 800 mg - After 8 hours, the body eliminates 50% of the drug. - Remaining drug after 8 hours: 800 mg * 0.5 = 400 mg 2. **Second Dose:** - New dose after 8 hours: 800 mg - Total drug amount in the system right after the second dose: 400 mg (remaining from first dose) + 800 mg = 1200 mg - After the next 8 hours, the body eliminates 50% of the drug. - Remaining drug after 8 hours: 1200 mg * 0.5 = 600 mg 3. **Third Dose:** - New dose after another 8 hours: 800 mg - Total drug amount in the system right after the third dose: 600 mg (remaining from second dose) + 800 mg = 1400 mg - After the next 8 hours, the body eliminates 50% of the drug. - Remaining drug after 8 hours: 1400 mg * 0.5 = 700 mg So, after three doses, there will be **700 mg** of the drug in your system.
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