Question: can you help i'm so confused. please use basic calculus rules. V. A mixing problem in medicine: A patient is given morphine intra- venously at

can you help i'm so confused. please use basic calculus rules.

V. A mixing problem in medicine: A patient is given morphine intra- venously at the rate of r milligrams per hour. (The constant r is unspecified for now.) Morphine is absorbed from the bloodstream of the patient at a rate equal to 34.7% of the amount in the bloodstream per hour. (a) Let A(t) be the amount of morphine, in mg, in the patient's blood- stream after t hours. Find a differential equation for A(t). (b) Find any equilibrium solutions of the differential equation. (c) Initially, there is no morphine in the patient's bloodstream. Find the solution of the differential equation that satisfies the appropriate initial condition. (d) What happens to A(t) after a long time? Justify your answer. (e) At what rate r should the patient be given morphine intravenously so that the amount of morphine in the bloodstream approaches 8.0 milligrams? MORE ON THE NEXT PAGE 2

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