Oral antibiotics In Example 1.3.7 we studied a model for antibiotic use in sinus infections. If x is the amount of antibiotic taken orally (in mg), then the function h(x) gives the amount entering the bloodstream through the stomach. If x mg reaches the bloodstream, then g(x) gives the amount that survives filtration by the liver. Finally, if x mg survives filtration by the liver, then f(x) is absorbed into the sinus cavity. Thus, for a given dose x, the amount making it to the sinus cavity is A(x) = f(g(h(x))). Suppose that a dose of 500 mg is given, h(500) = 8, g(8) = 2, f(2) = 1.5, and h'(500) = 2.5, g'(8) Calculate A' (x) and interpret your answer. = 4, and f'(2) = 1.

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