Leland got stung by a bee at a picnic. He took a 50-milligram dose of medicine to help relieve the swelling and itching. The medicine has a half-life of 8 hours. He was very sleepy the rest of the day and wondered how long the medicine would stay in his system. 1. Leland learns that he will finally stop feeling sleepy from his medicine when there is less than 1 milligram of the medicine in his system. When will that be? Show your work. 2. What percent of medicine remains in Leland’s system after each hour? Show your work. 3. When will the medicine be completely out of Leland’s system? Explain your thinking
Leland got stung by a bee at a picnic. He took a 50-milligram dose of medicine to help relieve the swelling and itching. The medicine has a half-life of 8 hours. He was very sleepy the rest of the day and wondered how long the medicine would stay in his system. 1. Leland learns that he will finally stop feeling sleepy from his medicine when there is less than 1 milligram of the medicine in his system. When will that be? Show your work. 2. What percent of medicine remains in Leland’s system after each hour? Show your work. 3. When will the medicine be completely out of Leland’s system? Explain your thinking
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter4: Exponential And Logarithmic Functions
Section: Chapter Questions
Problem 13CC
Related questions
Question
Leland got stung by a bee at a picnic. He took a 50-milligram dose of medicine to help relieve the swelling and
itching. The medicine has a half-life of 8 hours. He was very sleepy the rest of the day and wondered how long
the medicine would stay in his system.
1. Leland learns that he will finally stop feeling sleepy from his medicine when there is less than 1 milligram
of the medicine in his system. When will that be? Show your work.
2. What percent of medicine remains in Leland’s system after each hour? Show your work.
3. When will the medicine be completely out of Leland’s system? Explain your thinking.
Expert Solution
Step 1
Sol:-
- To determine when there is less than 1 milligram of the medicine in Leland's system, we need to use the concept of half-life. After one half-life, half of the initial dose remains in the body. So, after 8 hours, Leland will have 25 milligrams of the medicine remaining in his system (50 mg / 2). After another 8 hours (16 hours total), he will have 12.5 milligrams of the medicine remaining (25 mg / 2). Continuing this pattern, we can create the following table:
| Time (hours) | Amount of medicine remaining (milligrams) |
|---|---|
| 0 | 50 |
| 8 | 25 |
| 16 | 12.5 |
| 24 | 6.25 |
| 32 | 3.125 |
| 40 | 1.5625 |
| 48 | 0.78125 |
| 56 | 0.390625 |
| 64 | 0.1953125 |
| 72 | 0.09765625 |
Therefore, Leland will finally stop feeling sleepy from the medicine after 72 hours (3 days).
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