Question: A drug is administered intravenously at a constant rate of r mg/hour and is excreted at a rate proportional to the quantity present, with constant of proportionality α > 0.
(a) Solve a differential equation for the quantity, Q, in milligrams, of the drug in the body at time t hours. Assume there is no drug in the body initially. Your answer will contain r and α. Graph Q against t. What is Q∞, the limiting long-run value of Q?
(b) What effect does doubling r have on Q∞? What effect does doubling r have on the time to reach half the limiting value, ½ Q∞?
(c) What effect does doubling α have on Q∞? On the time to reach ½ Q∞?