A patient is given the drug theophylline intravenously at a rate of 43.2 mg/hour to relieve acute asthma. The rate at which the drug leaves the patient’s body is proportional to the quantity there, with proportionality constant 0.082 if time, t, is in hours. The patient’s body contains none of the drug initially.
(a) Describe in words how you expect the quantity of theophylline in the patient to vary with time.
(b) Write a differential equation satisfied by the quantity of theophylline in the body, Q(t).
(c) Solve the differential equation and graph the solution. What happens to the quantity in the long run?