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.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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Transcribed Image Text: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
(8+4)2
2 X
(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.
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