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Math Help - To find the constant?

  1. #1
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    Question To find the constant?

    The concentration of a certain drug in the bloodstream t hours after the drug is administered is given by c(t)=12te^-bt ng/ml where b is some positive constant.Suppose that the drug reached maximum concentration exactly after four hours after being administered.Find the constant b.
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    Quote Originally Posted by mathcalculushelp View Post
    The concentration of a certain drug in the bloodstream t hours after the drug is administered is given by c(t)=12te^-bt ng/ml where b is some positive constant.Suppose that the drug reached maximum concentration exactly after four hours after being administered.Find the constant b.
    c(t)=12te^{-bt}

    Differentiate by applying the product rule.

    c'(t)=-b12te^{-bt}+12e^{-bt}

    You're given that this function is maximum at t=4

    c'(4)-48be^{-4b}+12e^{-4b}=0

    48b=12

    b=\frac{1}{4}
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