Question

Chapter 9, Section 9.5, Question 015 A patient is given the drug theophylline intravenously at a rate of 43.2 mg/hour to relieve acute asthma. You can imagine the drug as enteringa compartment of volume 35,000 ml. (This is the volume of the part of the body through which the drug circulates) The rate at which the drug leaves the patient is proportional to the quantity there, with proportionality constant 0.082 if time, t, is in hours. Assume the patient's body contains none of the drug initially. [Note: Concentration Quantity/Volume. (a) Choose all statements that describe how the quantity of theophylline in the patient varies with time The quantity decreases with time at a decreasing rate. O The quantity increases with time at a constant rate The quantity of the drug in the body will eventually approach a constant amount The quantity increases with time at an increasing rate. The quantity decreases with time at a constant rate. The quantity increases with time at a decreasing rate. The quantity decreases with time at an increasing rate The quantity of the drug in the body will eventually be zero. The quantity stays constant over time (b) Write a differential equation satisfied by the concentration of the drug, Q(t) Enter the exact answer (c) Solve the differential equation Rou nd non-integer values to three decimal places.

Answer 1

(a). The quantity Q(t) of drug in the body, after t hours is Q(t) = 43.2t –(0.082)*43.2 t mg = 0.918 * 43.2 t mg = 39.6576t mg

Therefore, the quantity of drug increses with time at a constant rate. The 2^nd option is the correct answer.

(b). We have Q(t) = 39.6576t so that dQ/dt = 39.6576. Further, Q(t) = 39.6576t = t(dQ/dt) .