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Pharmacology When a drug is administered orally, the amount of the drug present in the bloodstream of the patient can be modeled by a function of the form
C(t) = ate^{-bt}
Where C(t) is the concentration of the drug in milligrams per liter (mg/L), is the number of hours since the drug was administered, and a and b are positive constants. For a 300-milligram dose of the asthma drug aminophylline, this function is
C(t) = 4.5te^{-0.275t}.
(a) How much of this drug is present in the bloodstream at time t = 0? Why does this answer make sense in the context of the problem?
(b)How much of this drug is present in the bloodstream after 1 hour?
(c) Sketch a graph of this function, either by hand or using a graphing utility, with ranging from 0 to 20.
(d)What happens to the value of the function as t→ ∞? Does this make sense in the context of the problem? Why?
(e) Use a graphing utility to find the time when the concentration of this drug reaches its maximum.
(f) Use a graphing utility to determine when the concentration of this drug reaches 3 mg L for the second time. (This will occur after the concentration peaks.)
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