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19 December, 02:28

The? half-life of a certain tranquilizer in the bloodstream is 4242 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. 19 December, 02:46
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    For this problem, we use the formula for radioactive decay which is expressed as follows:

    An = Aoe^-kt

    where An is the amount left after time t, Ao is the initial amount and k is a constant.

    We calculate as follows:

    An = Aoe^-kt

    0.5 = e^-k (42 hrs)

    k = 0.0165 / hr

    An = Aoe^-kt

    .86 = e^-0.0165 (t)

    t = 9.14 hrs
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