North Carolina School of Science and Mathematics
Distance Education and Extended Programs
Headache Medicine Problem and Exercises
You have a headache and decide to take a 200-mg over-the-counter headache medicine tablet to
relieve it. The ibuprofen in the pill is absorbed into your system and stays there until it is
metabolized and filtered out by the liver and kidneys. Every 4 hours, your body removes 67% of
the ibuprofen that was in your body at the beginning of that 4-hour time period.
1. Write a recursive system that represents the amount of ibuprofen in your body at any time.
How much of the ibuprofen will have remained in your system 24 hours after taking the 200mg tablet?
2. Suppose that the tablet contained 250 mg instead of 200. How much would be in your body
after 24 hours?
3. Suppose that your kidneys filter only 50% of the ibuprofen in 4 hours. If you take a 200-mg
tablet, how much would you have in your body after 24 hours?
4. Write a sentence to interpret the following recursive systems in the context of this problem.
Find how much ibuprofen remains after 24 hours. The domain of 𝐷𝑛 is 𝑛 = 1, 2, 3, …
a. 𝐷0 = 300,
𝐷𝑛 = 𝐷𝑛−1 − 0.8𝐷𝑛−1
b. 𝐷0 = 150,
𝐷𝑛 = 𝐷𝑛−1 − 0.2𝐷𝑛−1
c. 𝐷0 = 500,
𝐷𝑛 = 0.2𝐷𝑛−1
Adapted from Contemporary Precalculus through Applications by the North Carolina School of Science and
Mathematics, Everyday Learning Corporation, 2000