A drug administered to a patient produces a concentration in the blood stream given by c(t) = Ate-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 maximum safe concentration, and when does this maximum occur?
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 this second injection should be given.
c. Assume that the concentration from consecutive injections is addictive and that 75% of the amount originally injected is administered in the second injection. When is it time for the third injection?