Pharmacokinetics is the study of how drugs are absorbed into, distributed through, metabolized by and excreted from the human body. Some drug processes can be approximately modeled by a “one compartment” model of the body in which V is the volume of the compartment,  C(t)  is the drug concentration in that compartment,   k  e    is a rate constant for excretion of the drug from the compartment and   k  0    is the infusion rate at which the drug enters the compartment.

(a) Write a differential equation in which the infusion rate is the excitation and the drug concentration is the response.

(b) Let the parameter values be  ke = 0.4   hr   −1 , V = 20   l and   k  0    = 200 mg/hr (where “l” is the symbol for “liter”). If the initial drug concentration is  C (0)  = 10 mg/l , plot the drug concentration as a function of time (in hours) for the first 10 hours of infusion. Find the solution as the sum of the zeroexcitation response and the zero-state response.