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Math - Exponential Decay

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Radium decays exponentially. Its half-life is 1,690 years. How long will it take for a 50-gram sample of radium to be reduced to 5 grams?


1/2P = Pe^(-1690k)

(ln1/2)/(-1690) = k

4 x 10^-4 = k


5 = 50e^-kt

ln0.1 = -kt

ln0.1/-k = t

5,630 years = t


...but textbook answer is 5,614 years. Where did I go wrong?

  • Math - Exponential Decay -

    I got 5616 using 4.1 * 10^-4 for k

    You did it right but did not carry the same number of significant figures.

    it is easier to use a^-b = 1/a^b in a case like this
    1/10 = e^-kt
    becomes
    e^kt = 10
    t = ln 10/k = 2.303/.00041

  • Math - Exponential Decay -

    your calculator. Set it on scientific, so the k is equal to 4.101E-4

    With that, I get 5615 years.

  • Math - Exponential Decay -

    I, too, get 5615.

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