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A drug is administered intravenously at a constant rate of r mg/hour and is excreted at a rate proportional to the quantity present, with constant of proportionality k > 0. (a) Set up a differential equation for the quantity, Q, in milligrams, of the drug in the body at time t hours. Your answer will contain the unknown constants r and k. r-kQ Q': = (b) Solve this differential equation, assuming there is no drug in the body initially. Your answer will contain r and k. - e-kt) Q = k (c) What is the limiting long-run value of Q? lim Q(t) = 1 k

A drug is administered intravenously at a constant rate of r mg/hour and is excreted at a rate proportional to the quantity present, with constant of proportionality k > 0. (a) Set up a differential equation for the quantity, Q, in milligrams, of the drug in the body at time t hours. Your answer will contain the unknown constants r and k. r-kQ Q': = (b) Solve this differential equation, assuming there is no drug in the body initially. Your answer will contain r and k. - e-kt) Q = k (c) What is the limiting long-run value of Q? lim Q(t) = 1 k

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A drug is administered intravenously at a constant rate of r mg/hour and is excreted at a rate proportional to the quantity present, with constant of proportionality k > 0. (a) Set up a differential equation for the quantity, Q, in milligrams, of the drug in the body at time t hours. Your answer will contain the unknown constants r and k. Q' r-kQ (b) Solve this differential equation, assuming there is no drug in the body initially. Your answer will contain r and k. Q = ² (1 - e-kt) (c) What is the limiting long-run value of Q? lim Q(t) t→∞ r|k
Transcribed Image Text:A drug is administered intravenously at a constant rate of r mg/hour and is excreted at a rate proportional to the quantity present, with constant of proportionality k > 0. (a) Set up a differential equation for the quantity, Q, in milligrams, of the drug in the body at time t hours. Your answer will contain the unknown constants r and k. Q' r-kQ (b) Solve this differential equation, assuming there is no drug in the body initially. Your answer will contain r and k. Q = ² (1 - e-kt) (c) What is the limiting long-run value of Q? lim Q(t) t→∞ r|k
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