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15 November, 19:25

A certain radioactive isotope decays at a rate of 2% per 100 years. If t represents the amount of the isotope left then the equation for the situation is

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  1. 15 November, 21:05
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    y=y0e^-0.0002t
  2. 15 November, 23:07
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    A certain isotope decays at a rate of 2%per 100 years. If t represent the time in years and y represent the amount of the isotope left then the equation for the situation is y=y0e^-0.0002t. In how many years will there be 86% of the isotope left?

    .

    Let x = initial amount

    then our formula is

    .86x = xe^ (-0.0002t)

    .

    Notice, if we divide both sides by x, we eliminate our unknown:

    .86 = e^ (-0.0002t)

    Solving for x, we take the ln of both sides:

    ln (.86) = - 0.0002t

    ln (.86) / (-0.0002) = t

    754.114 years = t
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