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Hydrocodone bitartrate is used as a cough suppressant. After the drug is fully absorbed, the quantity of drug in the body decreases at a rate proportional to the amount left in the body, with constant of proportionality . Suppose that the half-life of hydrocodone bitartrate in the body is 3.7 hours, and that the oral dose taken is 12 mg.

(a) Write a differential equation for the quantity, , of hydrocodone bitartrate in the body at time , in hours, since the drug was fully absorbed.

  • calculus -

    amount = 12 (1/2)^(t/3.7) where t is in hours.

  • calculus -

    However, to answer the question,

    da/dt = ka

    The boundary conditions will reveal that
    k = ln(1/2)/3.7

  • calculus -

    Oops forgot about the 15. Toss it in as needed.

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