Morphine is often used as a pain-relieving drug. The halflifeof morphine in the body is
Chapter 11, Problem 17(choose chapter or problem)
Morphine is often used as a pain-relieving drug. The halflifeof morphine in the body is 2 hours. Suppose morphineis administered to a patient intravenously at a rateof 2.5 mg per hour, and the rate at which the morphine iseliminated is proportional to the amount present.(a) Use the half-life to show that, to three decimalplaces, the constant of proportionality for the rateat which morphine leaves the body (in mg/hour) isk = 0.347.(b) Write a differential equation for the quantity, Q, ofmorphine in the blood after t hours.(c) Use the differential equation to find the equilibriumsolution. (This is the long-term amount of morphinein the body, once the system has stabilized.)
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