Drug infusion The delivery of a drug (such as an
Chapter , Problem 52(choose chapter or problem)
Drug infusion The delivery of a drug (such as an antibiotic) through an intravenous line may be modeled by the differential equation m_1t2 + km1t2 = I, where m1t2 is the mass of the drug in the blood at time t 0, k is a constant that describes the rate at which the drug is absorbed, and I is the infusion rate. a. Show by substitution that if the initial mass of drug in the blood is zero 1m102 = 02, then the solution of the initial value problem is m1t2 = I k 11 - e-kt2. b. Graph the solution for I = 10 mg>hr and k = 0.05 hr-1. c. Evaluate lim tS_ m1t2, the steady-state drug level, and verify the result using the graph in part (b).
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