A mathematical model for the rate at which a drug disseminates into the bloodstr

Question

A mathematical model for the rate at which a drug disseminates into the bloodstream is given by dx(t)/dt = r - kx(t), where r and k are positive constants. The function x(t) describes the concentration of the drug in the bloodstream at time t. Assuming r = 0.3, k = 0.1, (a) Sketch the phase diagram to find the limiting value of x(t) as t tends to infinity. Find the particular solution of the initial value problem x(0) = 0. Compute the limiting value of x(t) as t tends to infinity? Sketch the solution and verify your prediction in part (a).

Explanation / Answer

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