Question

A patient who has asthma is given a continuous infusion of theophylline to relax and open the air passages in his lungs. The desired steady-state level of theophylline in the patient’s bloodstream is 15 mg/L. The average half-life of theophylline is about four hours, and the patient has 5.6 L of blood in his body. This situation can be modeled by the differential equation dy/dt=a-by, where y left-parenthesis t right-parenthesis is the amount of theophylline in the blood plasma at time t (in hours), the clearance rate constant of the theophylline is b=0.17, and the infusion rate is a=14.28 mg/h. Determine how long it takes for the concentration of theophylline to be 3 mg/L. Round your answer to two decimal places.

Answer 1