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Math Help - exponential decay

  1. #1
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    exponential decay

    A dosage of Q units of a certain drug is administered daily to a patient. If the amount of the drug in the bloodstream after n days is given by Qe^-kn where k is a constant, find:

    (i) The value of k if the amount of drug found in the bloodstream has halved after 1 day prior to administering the second dosage. Express your answer to three decimal places.

    (ii) Hence find the amount of drug found in the bloodstream after 15 days, prior to administering the next dosage

    Teacher said something about this question following simmilar to a supperannuation process but i don't understand. I need help with both parts.
    Last edited by Wullz16; July 24th 2010 at 02:47 AM.
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  2. #2
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    Quote Originally Posted by Wullz16 View Post

    (i) The value of k if the amount of drug found in the bloodstream has halved after 1 day prior to administering the second dosage. Express your answer to three decimal places.
    Q=Q_0e^{-kn}

    From the information given

    \frac{Q_0}{2}=Q_0e^{-k\times 1}

    \frac{1}{2}=e^{-k}

    \ln\frac{1}{2}=-k

    k = -\ln\frac{1}{2}

    Quote Originally Posted by Wullz16 View Post
    (ii) Hence find the amount of drug found in the bloodstream after 15 days, prior to administering the next dosage
    Sub in k as found above into Q=Q_0e^{-k\times 1} and solve for Q when n=15.
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