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Mathematics, 19.06.2020 15:57 jxeidy8284
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 Q against t. What is Q?, the limiting long-run value of Q?
Q?=
If r is doubled (to 2r), by what multiplicative factor is Q? 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, 12Q?, changed?
t (to 12Q?), for 2r) = t (to 12Q?), 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 12Q??
t (to 12Q?), for 2k) = t (to 12Q?), for k)
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A drug is administered intravenously at a constant rate of r mg/hour and is excreted at a rate propo...
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