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Unformatted text preview: r 10 days. (a) Determine the differential equation that describes the number of viewers who are aware of the product at time t . (b) Determine the solution of the differential equation from part (a) that satisﬁes the initial condition P (0) = 0. (c) How long will it take for 90% of the population to be aware of the product? 44. A drug is fed intravenously into a patient’s bloodstream at the constant rate r . Simultaneously, the drug diffuses into the patient’s body at a rate proportional to the amount of drug present. (a) Determine the differential equation that describes the amount Q(t ) of the drug in the patient’s bloodstream at time t . (b) Determine the solution Q = Q(t ) of the differential equation found in part (a) that satisﬁes the initial condition Q(0) = 0. (c) Find lim Q(t ).
t →∞ describes a population that undergoes periodic ﬂuctuations. Assume that P (0) = 1000 and ﬁnd P (t ). Use a graphing utility to draw the graph of P . (b) The differential equation dP =...
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- Spring '10