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23 December, 22:29

After the release of radioactive material into the atmosphere from a

nuclear power plant the hay in that country was contaminated by a

radioactive isotope (half-life 88 days). If it is safe to feed the hay

to cows when 15% of the radioactive isotope remains, how long

did the farmers need to wait to use this hay? Round to the nearest

day.

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Answers (1)
  1. 23 December, 22:55
    0
    The farmers had to wait 241 days

    Step-by-step explanation:

    The exponential decay model is

    y = A e^ (-k x)

    where

    k is the decaying constant x is the time it takes the radioactive material to decay y is the amount of radioactive isotope that is present

    Step 1:

    We first need to determine the decaying constant.

    1/2 = (1) e^ (-88k)

    ln (1/2) = - 88k

    -88k = - ln (2)

    k = ln (2) / 88k

    k = 7.88*10⁻³

    Therefore, the exponential decay model is

    y = A e^ ( - (7.88*10⁻³) x)

    Step 2:

    We must calculate the the time, x, by using the given information:

    y = A e^ ( - (7.88*10⁻³) x)

    0.15 = (1) e^ ( - (7.88*10⁻³) x)

    ln (0.15) = - (7.88*10⁻³) x

    x = ln (0.15) / - (7.88*10⁻³)

    x = 241 days

    Therefore, the farmers had to wait 241 days in order to use this hay.
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