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8 July, 00:20

In dogs, the drug carprofen has a half-life of 8 hours. If a veterinarian gives a dog an 80-milligram dose, how long will it take for the amount of carprofen in the dog to reach 10 milligrams?

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  1. 8 July, 00:23
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    The formula for half-life is given by:

    N (t) = Ne^ (-λt)

    or

    N (t) = N (1/2) ^ (t/τ)

    where:

    t=time

    N=initial amount

    N (t) = final amount

    τ=half-life

    thus the time taken for the drug to decay will be:

    10=80 (1/2) ^ (t/8)

    1/8 = (1/2) ^ (t/8)

    introducing natural logs;

    ln (1/8) = (t/8) ln (1/2)

    thus;

    [ln 1/8]/[ln 1/2]=t/8

    3=t/8

    t=3*8

    t=24 hours

    the answer is 24 hours
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