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29 July, 11:40

The decay rate for a radioactive isotope is 9.29.2 percent per year. find the half-life of the isotope. round to the nearest tenth of a year.

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  1. 29 July, 11:46
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    Exponential decay is given by the equation

    F = P (1 - r) ^t

    0.5 = 1 (1 - 0.092) ^t

    0.5 = (0.908) ^t

    log 0.5 = log (0.908) ^t

    log 0.5 = t * log 0.908

    t = (log 0.5) / (log 0.908)

    t = 7.18

    Answer: 7.2 years
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