The rate at which a drug is absorbed into the bloodstream is modeled by the first-order differential

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The rate at which a drug is absorbed into the bloodstream is modeled by the first-order differential equation
dC/dt = a - bC(t)
Where a and b are positive constants and C(t) denotes the concentration of drug in the bloodstream at time 1. Assuming that no drug is initially present in the bloodstream, find the limiting concentration of the drug in the bloodstream as t → ∞. How long does it take for the concentration to reach one-half of the limiting value?
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Differential Equations and Linear Algebra

ISBN: 978-0131860612

2nd edition

Authors: Jerry Farlow, James E. Hall, Jean Marie McDill, Beverly H. West

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