A person is given an injection of 300 milligrams of penicillin at time t = 0. Let f (t) 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 (t) = 300e^-0.6t.

(a) Give the differential equation satisfied by f(t)

(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?