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, ke is a rate constant for excretion of the drug from the compartment and k0 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 
(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 zero-excitation response and the zero-state response.
SOLUTION:
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