)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. Q = r/k * (1-e^(-kt)] Graph Q against t. What is Qoo, the limiting long-run value of Q? Q0 = r/k If r is doubled (to 2r), by what multiplicative factor is Q, increased? Qoo (for 2r) = 2 Qoo (for r) Similarly, if r is doubled te a by what multiplicative factor is the time it takes to reach half the limiting value, Q.0, changed? t (to Q0), for 2r) In(2)/In(0.5) (to Q00), for r) If k is doubled (that is, we use 2k instead of k), by what multiplicative factor is Q, increased? Qoo (for 2k) = 0.5 Q00 (for k) On the time to reach t (to Q0), for 2k)= 2 t (to Q00), for k)

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