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 k > 0. (Set up and) 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 k. Graph Q against t. What is Qo, the limiting long-run value of Q? If r is doubled (to 2r), by what multiplicative factor is Qo increased? Q∞ (for 2r) = Q. (for r) Similarly, if r is doubled (to 2r), by what multiplicative factor is the time it takes to reach half the limiting value, Q0, changed? t (to ±Q∞), for 2r) = t (to Q∞), for r) If k is doubled (that is, we use 2k instead of k), by what multiplicative factor is Q, increased? Q∞ (for 2k) = Q∞ (for k) On the time to reach Q∞? t (to ¿Q∞), for 2k) = t (to Q∞), for k)

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