North Carolina School of Science and Mathematics
Distance Education and Extended Programs
Lesson 1 Homework Problems
1. Your doctor instructs you to take two 200-mg ibuprofen tablets every 4 hours for 3 days for a
pain in your knee. Your body eliminates 67% of the ibuprofen every 4 hours.
a. Write a recursive system that represents the amount of ibuprofen in your body at any
time.
b. How long does it take the ibuprofen to reach the therapeutic level of 450 mg?
c. What is the equilibrium level if you take two 200-mg tablets every 4 hours over a long
period of time?
d. You don’t like taking so much at one time, so you decide not to follow the doctor’s
instructions and take only one 200-mg ibuprofen tablet every 4 hours for 6 days.
Write a recursive system that represents this situation.
e. After the 6 days, your knee has not responded to the medication. What could have
happened?
2. If you take your medication every 4 hours, determine the amount of ibuprofen in your body
after 2 days and the equilibrium level resulting from each of the following recursive systems.
In some cases, the initial dosage differs from subsequent doses. In each exercise, the domain
of 𝐷𝑛 is 𝑛 = 1, 2, 3, …
a. 𝐷0 = 200,
𝐷𝑛 = 𝐷𝑛−1 − 0.4𝐷𝑛−1 + 200
b. 𝐷0 = 800,
𝐷𝑛 = 0.6𝐷𝑛−1 + 200
c. 𝐷0 = 600,
𝐷𝑛 = 0.4𝐷𝑛−1 + 300
3. Each of the recursive systems in #2 above can be written in the form
𝐷0 = 𝑎,
𝐷𝑛 = (1 − 𝑟)𝐷𝑛−1 + 𝑏,
𝑛 = 1, 2, 3, …
a. What does r represent? Why is r between 0 and 1?
b. By looking back at the results of #2 and by trying other variations, determine the effect
of changing a, r and b on the amount of ibuprofen in your body after 5 days.
c. Determine the equilibrium level in terms of a, r, and b. Recall that 𝐷𝑛 = 𝐷𝑛−1 when
equilibrium is reached.
d. Use the result in part c) to determine the equilibrium level of any medicine if you take
200 mg every 4 hours and your kidneys filter our 50% of the medicine in your body
every 4 hours.
Adapted from Contemporary Precalculus through Applications by the North Carolina School of Science and
Mathematics, Everyday Learning Corporation, 2000