A patient is given a drug intravenously at a rate of 43.2mg/hr. The rate at whic

Question

A patient is given a drug intravenously at a rate of 43.2mg/hr. The rate at which the drug leaves the patients's body is proportional to the quantity there, with proportionality constant 0.082 if time is ,t, in hours. The patients's body contains none of the drug initially. a) describe in words how you expect the quantity of the drug in the patient to vary with time. b) write a differential equation satisfied by the quantity of the drug in the body, Q(t). c)solve the differential equation and graph the solution. What happens to the quantity in the long run. EXTREMELY URGENT!!!

Explanation / Answer

Let P be the amount of theophylline in the patient. dP/dt = 43.2 - 0.082 P ......... rate of P_in - rate of P_out dP/dt + 0.082 P = 43.2 d/dt [ e^(0.082t) P ] = 43.2 e^(0.082t) e^(0.082t) P = 526.829 e^(0.082t) + C P = Ce^(-0.082t) + 526.829 ..... C to be determined by an initial condition Answer: dP/dt = 43.2 - 0.082 P .......

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