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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 3.9 hours, and that the oral dose taken is 11 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.