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Math Help - Hint needed(and exam tomorrow). Applications of calculus in calculating medicine dose

  1. #1
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    Hint needed(and exam tomorrow). Applications of calculus in calculating medicine dose

    Hello everyone!

    I am doing the following question:

    The rate of decrease in the concentration of the drug in the bloodstream at time t hours is proportional to the amount x (mg) in the bloodstream at that time.

    a) Show that x=x_0e^{-kt}, where k is a positive constant and x_0 is the size of the dose.

    Ok, I did this part.

    Then comes the difficult part.

    b) Show that the amount of the drug in the bloodstream will never exceed (\frac{x_0}{1-e^-{kT}})

    I did this

    in the beginning of T=1
    the amount of drug is

    x_0e^{-k}+x_0

    in the beginning of T=2
    the amount of drug is
    x_0e^{-2k}+x_0e^{-k}+x_0

    Then I thought that this could be the sum of an infinite geometric progression. So the sum would approach the limit


    (\frac{x_0}{1-e^{-k}}), but I'm missing the T!

    Where am I going wrong?
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  2. #2
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    ---
    Last edited by seld; September 16th 2009 at 05:48 PM. Reason: incorrect
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