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Math Help - Half-life problem

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    Half-life problem

    The half-life of radioactive strontium-90 is approximately 32 years. In 1964, radioactive strontium-90 was released into the atmosphere during testing of nuclear weapons, and was absorbed into people's bones. How many years does it take until only 5 percent of the original amount absorbed remains?
    Last edited by cwarzecha; September 9th 2008 at 03:03 PM.
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    Quote Originally Posted by cwarzecha View Post
    The half-life of radioactive strontium-90 is approximately 32 years. In 1964, radioactive strontium-90 was released into the atmosphere during testing of nuclear weapons, and was absorbed into people's bones. How many years does it take until only 5 percent of the original amount absorbed remains?
    You have
    A(t) = A_0 \left ( \frac{1}{2} \right )^{t/t_{1/2}}
    where t_{1/2} = 32. We are looking for 5% to be left so we know that
    \frac{A(t)}{A_0} = 0.05

    So solve
    \frac{A(t)}{A_0} = 0.05 = \left ( \frac{1}{2} \right )^{t/32}

    -Dan
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