Bioavailability is a term that refers to the fraction of an antibiotic dose taken orally that is absorbed into the bloodstream. Suppose that, for a dosage of x mg, the bioavailability is h(x) = x mg. If x mg enters the bloodstream, suppose that the amount eventually absorbed into the site of an infection is given by g(x) = 8x/(x + 8) mg. Finally, if x mg is absorbed into the site of an infection, suppose that the number of surviving bacteria is given by f(x) = 3200/(32+x2), measured in colony forming units, CFU. (a) Derive the function that relates oral dosage to the number of surviving bacteria using composition of functions. 3200 + 4x 2 x x+4 (b) Suppose the antibiotic is instead administered by injection. Derive the function that relates dosage to the number of surviving bacteria using composition of functions.

Bioavailability is a term that refers to the fraction of an antibiotic dose taken orally that is absorbed into the bloodstream. Suppose that, for a dosage of x mg, the bioavailability is h(x) = x mg. If x mg enters the bloodstream, suppose that the amount eventually absorbed into the site of an infection is given by g(x) = 8x/(x + 8) mg. Finally, if x mg is absorbed into the site of an infection, suppose that the number of surviving bacteria is given by f(x) = 3200/(32+x2), measured in colony forming units, CFU. (a) Derive the function that relates oral dosage to the number of surviving bacteria using composition of functions. 3200 + 4x 2 x x+4 (b) Suppose the antibiotic is instead administered by injection. Derive the function that relates dosage to the number of surviving bacteria using composition of functions.

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

ChapterP: Prerequisites

SectionP.4: Factoring Polynomials

Problem 84E: The rate of change of an autocatalytic chemical reaction is kQxkx2 where Q is the amount of the...

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