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25 February, 19:11

The half-life of a certain tranquilizer in the bloodstream is 5050 hours. how long will it take for the drug to decay to 8686 % of the original dosage? use the exponential decay model, upper a equals upper a 0 e superscript kta=a0ekt , to solve.

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  1. 25 February, 19:12
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    Using the exponential decay model; we calculate "k"

    We know that "A" is half of A0

    A = A0 e^ (k * 5050)

    A/A0 = e^ (5050k)

    0.5 = e^ (5055k)

    In (0.5) = 5055k

    -0.69315 = 5055k

    k = - 0.0001371

    To calculate how long it will take to decay to 86% of the original mass

    0.86 = e^ (-0.0001371t)

    In (0.86) = - 0.0001371t

    -0.150823 = - 0.0001371 t

    t = 1100 hours
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