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Hydrocodone bitartrate is used as a cough suppressant. After thedrug is fully absorbed, the quantity of drug in the body decreasesat a rate proportional to the amount left in the body, withconstant of proportionality "k". Suppose that the half-life ofhydrocodone bitartrate in the body is 3.9 hours, and that the oraldose taken is 9 mg. a)Write a differential equation for thequantity, "Q" , of hydrocodone bitartrate in the body at time "t",in hours, since the drug was fully absorbed.b)Solve yourdifferential equation, assuming that at the patient has justabsorbed the full 9 mg dose of the drug. c) Use the half-life tofind the constant of proportionality "k". d) How much of the 9 mgdose is still in the body after 12 hours?

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Jarrod Robel
Jarrod RobelLv2
28 Sep 2019

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