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Exponential decay word problem (check work)

  1. Sep 3, 2006 #1
    At time t hours after taking the cough suppressant hydrocodone bitartrate, the amount, A, in mg, remaining in the body is given by A = 10(0.82)t.

    (a) What was the intial amount taken?

    10 mg

    (b) What percent of the drug leaves the body each hour?


    (c) How much of the drug is left in the body 6 hours after the dose is administered?

    A = 10(0.82)6
    A = 3.04 mg

    (d) How long is it until only 1 mg of the drug remains in the body?

    1 = 10(0.82)t
    1/10 = 0.82t
    ln (1/10) = t ln0.82
    t = ln (1/10) / ln0.82
    t = 11.6028 hours

    Are these correct?
  2. jcsd
  3. Sep 4, 2006 #2


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    Staff Emeritus
    Science Advisor

    Certainly looks correct. It would help if one shows all work, e.g. on problem b, but the answer is correct.
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