O ral 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 hsxd gives the amount entering the bloodstream through the stomach.

If x mg reaches the bloodstream, then tsxd gives the amount that survives filtration by the liver. Finally, if x mg survives filtration by the liver, then f sxd is absorbed into the sinus cavity. Thus, for a given dose x, the amount making it to the sinus cavity is Asxd − f stshsxddd. Suppose that a dose of 500 mg is given, hs500d − 8, ts8d − 2, f s2d − 1.5, and h9s500d − 2.5, t9s8d − 14

, and f 9s2d − 1.

Calculate A9sxd and interpret your answer.