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Math Help - Half Life Question

  1. #1
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    Half Life Question

    I have an answer that I doubt (I do not have a textbook for an answer).

    Here is the question: A radioactive substance has a half life of 20 days

    i) How much time is required so that only 1/32 of the original amount remains?

    My answer: T = 100 days?

    ii) Find the rate of decay at this time.

    -0.001/day?
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  2. #2
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    Quote Originally Posted by CuriousThought View Post
    I have an answer that I doubt (I do not have a textbook for an answer).

    Here is the question: A radioactive substance has a half life of 20 days

    i) How much time is required so that only 1/32 of the original amount remains?

    My answer: T = 100 days?

    ii) Find the rate of decay at this time.

    -0.001/day?

    Assume we begin with a quantity x, so after 20 days we get \frac{x}{2}=xa^{20}\Longrightarrow a^{20}=\frac{1}{2}\Longrightarrow a=2^{-1\slash 20} ,and from here \frac{x}{32}=x\left(2^{-1\slash 20}\right)^t\Longrightarrow t=\frac{-\ln(32)}{\ln(2^{-1\slash 20})}=100 , and your answer's correct

    Tonio
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