Reference no: EM131611058

Question: Morphine is often used as a pain-relieving drug. The halflife of morphine in the body is 2 hours. Suppose morphine is administered to a patient intravenously at a rate of 2.5 mg per hour, and the rate at which the morphine is eliminated is proportional to the amount present.

(a) Use the half-life to show that, to three decimal places, the constant of proportionality for the rate at which morphine leaves the body (in mg/hour) is k = -0.347.

(b) Write a differential equation for the quantity, Q, of morphine in the blood after t hours.

(c) Use the differential equation to find the equilibrium solution. (This is the long-term amount of morphine in the body, once the system has stabilized.)