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Math Help - Decay

  1. #1
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    Cool Decay

    Suppose the decay for a radioactive element is known to be y=y e^-0.24t, with t in years. About how long will it take for a sample of this element to decay to 70% of its original amount?
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  2. #2
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    Quote Originally Posted by CalcQueen View Post
    Suppose the decay for a radioactive element is known to be y=y e^-0.24t, with t in years. About how long will it take for a sample of this element to decay to 70% of its original amount?
    I assume you mean y = {\color{red}y_0} e^{-0.24t}.

    The initial amount is y_0. So substitute y = 0.7 y_0 and solve for t:

    0.7 y_0 = y_0 e^{-0.24t} \Rightarrow 0.7 = e^{-0.24t} etc.
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