Suppose that t hours after an antibiotic is administered orally, its concentration in the patient’s bloodstream is given by a surge function of the form C(t) = Ate^−kt, where A and k are positive constants and C is measured in micrograms per milliliter of blood. Blood samples are taken periodically, and it is determined that the maximum concentration of drug occurs 2 hours after it is administered and is 10 micrograms per milliliter.

a. Use this information to determine A and k.

b. A new dose will be administered when the concentration falls to 1 microgram per milliliter. When does this occur?