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Math Help - Exponential decay

  1. January 28th 2010, 08:58 AM #1
    arandomnerd
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    Unhappy Exponential decay

    The decay of a radioactive substance is governed by the relation

    N = Pe^(-kt)

    where P is the amount at time t=0
    N is the amount at time t
    k is the decay constant

    For a certain substance 14% has decayed in 23 years, calculate the half life of the substance.
    How long will it take 44% of the substance to decay?

    Please help, this is really puzzling me
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  2. January 28th 2010, 10:05 AM #2
    Black
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    Quote Originally Posted by arandomnerd View Post
    For a certain substance 14% has decayed in 23 years, calculate the half life of the substance.
    So we have

    N(23)=.86P=Pe^{23k}.

    Solve for k. To find the half-life t_{1/2}, we have

    .5P=Pe^{kt_{1/2}} \Longrightarrow t_{1/2}=\frac{\text{ln}(1/2)}{k}.

    Quote Originally Posted by arandomnerd View Post
    How long will it take 44% of the substance to decay?
    Solve for t in the equation

    .56P=Pe^{kt}.
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