The concentration of a certain drug in a patient’s bloodstream t hours after being administered orally is assumed to be given by the function C(t) = Ate^−kt, where C is measured in micrograms of drug per milliliter of blood. Monitoring devices indicate that a maximum concentration of 5 occurs 20 minutes after the drug is administered.

a. Use this information to find A and k.

b. What is the drug concentration in the patient’s blood after 1 hour?

c. At what time after the maximum concentration occurs will the concentration be half the maximum?

d. If you double the time in part (c), will the resulting concentration of drug be 1/4 the maximum? Explain.