A drug administered to a patient produces a concentration in the blood stream given by c(t) = At exp(-t/3) milligrams per milliliter, t hours after A units have been injected. The maximum safe...

A drug administered to a patient produces a concentration in the blood stream given by c(t) = At exp(-t/3) milligrams per milliliter, t hours after A units have been injected. The maximum safe concentration is 1 mg/ml.
(a) What amount should be injected to reach this safe concentration, and when does this maximum occur?
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(b) An additional amount of this drug is to be administered to the patient after the concentration falls to 0.25 mg/ml. Determine to the nearest minute, when the second injection should be given