Math CentralQuandaries & Queries


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 $t.$


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