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Math Help - exponential decay , word problem

  1. #1
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    exponential decay , word problem

    Exponential decay: The amount of a radioactive material present at time t decays at a rate proportional
    to the amount present at that time. The half life h is the time at which half of the material has decayed.
    The mathematical model for exponential decay is

      \displaystyle y(t) = y0 \frac{1}{2}^{\frac{t}{h}}

    Here y0 is the initial amount of the substance present. After  \frac{t}{h} half lives, the material has been successively halved  \frac{t}{h} times.

    Hint: recall that  a^{b} = e^{bln(a)}



    Uranium-238 has a half life of  4.5 \times 10^{9} years. Let A be an amount of Uranium-238. What fraction of A is the amount left after  10^{9} years?

    b. 238 grams of Uranium-238 contain Avogadro's number, approximately  6 \times   10^{23} atoms. Using this approximation for Avogadro's number, how many atoms of 238 grams of Uranium-238 will decay in the first
    year? In the second year?
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  2. #2
    MHF Contributor Unknown008's Avatar
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    Just substitute A into your formula.

    y(t) = Answer you're looking for
    yo = A
    t = 10^9
    h = 4.5 x 10^9

    b.

    Take your formula again. This time,
    y(1) = amount left after 1 year
    yo = 6 x 10^23
    t = 1
    h = 4.5 x 10^9

    and
    y(2) = amount left after 2 years
    yo = 6 x 10^23
    t = 2
    h = 4.5 x 10^9

    Number of atoms decayed = Initial atoms - Atoms left.

    EDIT: Typo in the second part of b. I put after 1 year again whilst it should be 2 years.
    Last edited by Unknown008; January 18th 2011 at 10:09 AM.
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  3. #3
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    Thanks for that, life saver.

    Dont know why I was thinking something else with this question....
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