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. = 7/1 (1 - e-kt) (c) What is the limiting long-run value of Q? lim Q(t) t→∞0 = r 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. Q' = r-kQ (b) Solve this differential equation, assuming there is no drug in the body initially. Your answer will contain r and k. = 7/1 (1 - e-kt) (c) What is the limiting long-run value of Q? lim Q(t) t→∞0 = r k
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 13EQ
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