Chapter 5.1, Problem 37E

Decay of Penicillin in the Bloodstream A person is given an injection of $300$ milligrams of penicillin at time $t=0$. Let $f\left(t\right)$ be the amount (in milligrams) of penicillin present in the person’s bloodstream $t$ hours after the injection. Then, the amount of penicillin decays exponentially, and a typical formula is $f\left(t\right)=300e^{-0.6t}$.

a. Give the differential equation satisfied by $f\left(t\right)$?

b. How much will remain at time $t=5$ hours?

c. What is the biological half-life of the penicillin (that is, the time required for half of a given amount to decompose) in this case?