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| Math Central | Quandaries & Queries |
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Question from Nancy, a student: After an injection, the concentration of drug in a muscle varies according to a function of time, f(t).Suppose that t is measured in hours and f(t)=e^-0.02t - e^-0.42t. Determine the time when the maximum concentration of drug occurs. |
Hi Nancy,
Differentiate $f(t) = e^{-0.02t} - e^{-0.42t},$ set the derivative equal to zero and simplify. You should be able to reach an expression of the form
\[e^{At} = B e^{Ct}.\]
Take the natural log of both sides to get
\[A t = \ln(B) + C t.\]
Solve for $t.$
Penny
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