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Math Help - Radioactive Decay

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    Radioactive Decay

    If 80% of a radioactive element remains radioactive after 250 years, what percent remains radioactive after 600 years? What is the half life of the element?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Neversh View Post
    If 80% of a radioactive element remains radioactive after 250 years, what percent remains radioactive after 600 years? What is the half life of the element?
    we use the formula A(t) = A_0e^{-rt}

    where A(t) is the amount remaining after time t, A_0 is the initial amount, and r is the decay constant.

    say A_0 = 1, then when t = 250, we have

    0.8 = e^{-250r}

    use that equation to find r.

    after that, you can answer the other questions (the half-life is easy, it is \frac {\ln 2}r)
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