math

Show that if a radioactive substance has a half life of T, then the corresponding constant k in the exponential decay function is given by k=-ln(2)/T

I'm confused about how to show that that is true.

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asked by lucy
  1. since the amount drops by 1/2 every T, the function is

    f(t) = (1/2)^(t/T)
    But, 1/2 = e^-ln2, so

    f(t) = (e^(-ln2))^(t/T))
    = e^(-ln2/T t)
    = e^(kt)

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    posted by Steve

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