# Applied Calculus 37(5)

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PynverZnevr1994

Mathematics

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(2 pts) 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 k. Suppose that the half-life of hydrocodone bitartrate in the body is 3.8 hours, and that the oral dose taken is 9 mg. (a) Write a differential equation for the quantity, Q, of hydrocodone bitartrate in the body at time t, in hours, since the drug was fully absorbed. e' = (Write your answer in terms of Q and t, e.g., Q' = 3t(1 – kQ).) (b) Solve your differential equation, assuming that at t = 0 the patient has just absorbed the full 9 mg dose of the drug. Q= (Your solution may include the constant of proporationality k, but should not include any other unspecified constant.) (c) Use the half-life to find the constant of proportionality, k. k= (d) How much of the 9 mg dose is still in the body after 12 hours? Amount =
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