Drug infusion The delivery of a drug (such as an antibiotic) through an intravenous line may be modeled by the differential equation m' (t) + km(t) = I, where m(t) is the mass of the drug in the blood at time t z 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 (m(0) = 0), then the solution of the initial value problem is m(t) = (1 – e*). b. Graph the solution for I = 10 mg/hr and k = 0.05 hr¯1. c. Evaluate lim m(t), the steady-state drug level, and verify the result using the graph in part (b).
Drug infusion The delivery of a drug (such as an antibiotic) through an intravenous line may be modeled by the differential equation m' (t) + km(t) = I, where m(t) is the mass of the drug in the blood at time t z 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 (m(0) = 0), then the solution of the initial value problem is m(t) = (1 – e*). b. Graph the solution for I = 10 mg/hr and k = 0.05 hr¯1. c. Evaluate lim m(t), the steady-state drug level, and verify the result using the graph in part (b).
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:Drug infusion The delivery of a drug (such as an antibiotic)
through an intravenous line may be modeled by the differential
equation m' (t) + km(t) = I, where m(t) is the mass of the drug
in the blood at time t z 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 (m(0) = 0), then the solution of the initial value
problem is m(t) = (1 – e*).
b. Graph the solution for I = 10 mg/hr and k = 0.05 hr¯1.
c. Evaluate lim m(t), the steady-state drug level, and verify the
result using the graph in part (b).
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