Question

Karey is prescribed 600 mg of a medication that decays at a rate of 40% per day, d, according to the equation mc020-1.jpg, where m is the amount of medication remaining in his body. Noelle takes the same medication five days earlier. The number of milligrams of medication in Noelle’s body is about what percentage of the number of milligrams in Karey’s body at any time after they have both taken the medication?
3.0%
7.8%
12.9%
46.7%

Answer 1

Let t be days after Karey takes the dose. Karey: 600(0.6)^t. Noelle (took it 5 days earlier): 600(0.6)^{t+5}.

Ratio = (600(0.6)^{t+5})/(600(0.6)^t) = (0.6)^5 ≈ 0.07776 = 7.776% ≈ 7.8%.

Answer: 7.8%.