Suppose that antibiotics are injected into a patient to treat a sinus infec- tion. The antibiotics circulate in the blood, slowly diffusing into the sinus cavity while simultaneously being filtered out of the blood by the liver. The following is a model for the concentration (in µg/mL) of the antibiotic in the sinus cavity as a function of time (in hours) since the injection. e-at – e-8t C(t) В —а where a and ß are constants with ß > a > 0. (a) occurs. (Your argument must use the first derivative test.) Using the first derivative test, find when the maximum concentration (b) (Your answer should be supported by a rigorous argument.) When does the rate of change of concentration begin to increase?
Suppose that antibiotics are injected into a patient to treat a sinus infec- tion. The antibiotics circulate in the blood, slowly diffusing into the sinus cavity while simultaneously being filtered out of the blood by the liver. The following is a model for the concentration (in µg/mL) of the antibiotic in the sinus cavity as a function of time (in hours) since the injection. e-at – e-8t C(t) В —а where a and ß are constants with ß > a > 0. (a) occurs. (Your argument must use the first derivative test.) Using the first derivative test, find when the maximum concentration (b) (Your answer should be supported by a rigorous argument.) When does the rate of change of concentration begin to increase?
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Suppose that antibiotics are injected into a patient to treat a sinus infec-
tion. The antibiotics circulate in the blood, slowly diffusing into the sinus cavity while
simultaneously being filtered out of the blood by the liver. The following is a model
for the concentration (in µg/mL) of the antibiotic in the sinus cavity as a function of
time (in hours) since the injection.
e-at – e-ßt
C(t)
В — а
where a and B are constants with ß > a > 0.
(a)
occurs. (Your argument must use the first derivative test.)
Using the first derivative test, find when the maximum concentration
(b)
(Your answer should be supported by a rigorous argument.)
When does the rate of change of concentration begin to increase?
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