A drug is administered intravenously at a constant rate of r mg/hour and is excreted at...

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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= Graph against t. What is Q∞, the limiting long-run value of Q? 200 = If r is doubled (to 2r), by what multiplicative factor is Q increased? Qoo (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, 20, changed? t (to Q∞), for 2r) = t (to 2%), for r) If k is doubled (that is, we use 2k instead of k), by what multiplicative factor is Qoo increased? Q∞ (for 2k) = On the time to reach 2∞? t (to 2%), for 2k) = Qoo (for k) t (to 2%), for k) 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= Graph against t. What is Q∞, the limiting long-run value of Q? 200 = If r is doubled (to 2r), by what multiplicative factor is Q increased? Qoo (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, 20, changed? t (to Q∞), for 2r) = t (to 2%), for r) If k is doubled (that is, we use 2k instead of k), by what multiplicative factor is Qoo increased? Q∞ (for 2k) = On the time to reach 2∞? t (to 2%), for 2k) = Qoo (for k) t (to 2%), for k)

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To set up the differential equation for the quantity Q of the drug in the body at time t well use the concept of exponential decay Let Qt be the quant... View the full answer