Answer to Question #79346 in Calculus for tshepho

Question

Intravenous infusion of glucose into the blood-stream of a patient is an important medical technique. To study this process, let G(t) be the amount of glucose in the patient’s blood stream t minutes after the process begins. Assume that glucose is infused into the bloodstream at a constant rate of k(in g/min). Also assume that at the same time, the glucose is converted and removed from the bloodstream at a rate proportional to the amount of glucose still present, with the proportionality constant r.(a) Write a first-order differential equation describing this process that should be satisfied by G(t).(b) Suppose that glucose is not present initially in the patient’s bloodstream; solve the differential equation in (a) above which satisfies the initial condition G(0) = 0.
(c) Find
lim t→∞G(t).