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8 October, 04:42

Carbon-14 is a radioactive isotope that decays exponentially at a rate of 0.0124 percent a year. How many years will it take for carbon-14 to decay to 10 percent of its original amount? The equation for exponential decay is At = A0e-rt.

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  1. 8 October, 07:39
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    100-0.0124=99.9876

    10%=1/10

    1/10P=P (0.999876) ^t

    divide both sides by P

    1/10=0.999876^t

    take ln of both sides

    ln (1/10) = t (ln (0.999876))

    divide both sides by (ln (0.999876))

    ln (1/10) / (ln (0.999876)) = t

    use calculator

    18568.08=t

    about 18568 years
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