And RT w be the number Return to Blackboard Hughes-Hallett, Applied Calculus, se

Question

And RT w be the number Return to Blackboard Hughes-Hallett, Applied Calculus, se US Help I System Announcements Unread) P&INTER; VERSION Chapter 9, Section 9.5, Question 01sbc Apatient is given the drug theophynine intravenously at a rate of 43.2 mghour to releve asthma. You can imagine the drug as entering a compartment of volume 35,000 ml (This is the acute volume of the part of the body through which the drug circulates The rate at which the drug leaves the patient is proportional the quantity with proportionalty constant 0082 to there, Assume the patient's body contains none of the drug initially. [Note Concentration QuantityNolume) Incorrect. (a) write a differential equation satisfied by the concentration of the drug, c(t) Enter the exact answer.

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

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