A patient is given a drug intravenously at a rate of 43.2 mg/hour. The drug enters a compartment volume or the volume of the part of the body of 35,000 ml. The rate at which the drug leaves the body

(mg/hour) is proportional to the quantity present, with proportionality constant 0.082 per hour. The patient doesnt have any drugs initially.
(a) Describe in words how you would expect the concentration of the drug in the patient to vary with time.
(b)Write a differential equation satisfied by the concentration of the drug, c(t).
(c)Solve the differentail equation.

I get dw/dt=36.8-0.048D as my equation and when i solve i get D=Aexp(-.048)=36.8

am I off any help would be greatly appreciated.

1 answer

  1. They want c(t), which represents the concentration present. Concentration is mass present divided by volume (with units of mg/ml). Let time t be in hours.
    dc/dt = (1/35,000)* [43.2 -35,000 c*0.082)
    = (1/35,000)*[43.2 - 2870 c)

    The steady state concentration (after very large t) is obtained when dc/dt= 0, and corresponds to
    c = 0.015 mg/ml

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