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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. = 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

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter6: Exponential And Logarithmic Functions
Section6.1: Exponential Functions
Problem 60SE: The formula for the amount A in an investmentaccount with a nominal interest rate r at any timet is...
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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 rand k. = / 1 (1 - e-ht) (c) What is the limiting long-run value of Q? lim Q(t) 0077 = 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 rand k. = / 1 (1 - e-ht) (c) What is the limiting long-run value of Q? lim Q(t) 0077 = r k
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