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Math Help - Exponential and Logarithmic functions

  1. #1
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    Exponential and Logarithmic functions

    Consider that the proportion of a radioactive material remaining after time t has elapsed is e^-kt where k is a positive constant; investigate the re;ationship between k and the half-life of the material.
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  2. #2
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    Re: Exponential and Logarithmic functions

    Hey tedwa64.

    Do you have the formula for radio-active decay either in function form or in DE form?
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  3. #3
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    Re: Exponential and Logarithmic functions

    Hey Chiro,
    Function form.
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  4. #4
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    Re: Exponential and Logarithmic functions

    You have to find the time it takes where the quantity is halved.

    So if you set up f(t0) = e^(-kt0) and f(t1) = e^(-kt1) then f(t1) = 1/2*f(t0) for some t1 > t0.

    We get 1/2 = e^(-k[t1-t0]). So we get -ln(2) = -k*[t1-t0] which means our half life time is t1-t0 = ln(2)/k.

    This is the time it takes for your quantity to reduce in half.
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