Chapter 10.3, Problem 43E

Periodic doses Suppose you take a dose of m mg of a particular medication once per day. Assume f equals the fraction of the medication that remains in your blood one day later. Just after taking another dose of medication on the second day, the amount of medication in your blood equals the sum of the second dose and he fraction of the first dose remaining in your blood, which is m + mf. Continuing in this fashion, the amount medication in your blood just after your nth dose is A_n = m + mf + ⋯ + mfⁿ⁻¹. For the given values of ^:and m, calculate A₅, A₁₀, A₃₀ and $\underset{n\to \infty }{\lim }{A}_n$. Interpret the meaning of the limit $\underset{n\to \infty }{\lim }{A}_n$.

43. ∫ = 0.25, m = 200 mg