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 ug/mL) of the antibiotic in the sinus cavity as a function of time (in hours) since the injection. e-at - e-Bt C(t) = B- a where a and B are constants with B> a > 0. Using the first derivative test, find when the maximum concentration occurs. (Your argument must use the first derivative test.) When does the rate of change of concentration begin to increase? (Your answer should be supported by a rigorous argument.)

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 ug/mL) of the antibiotic in the sinus cavity as a function of time (in hours) since the injection. e-at - e-Bt C(t) = B- a where a and B are constants with B> a > 0. Using the first derivative test, find when the maximum concentration occurs. (Your argument must use the first derivative test.) When does the rate of change of concentration begin to increase? (Your answer should be supported by a rigorous argument.)

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.7: Applications

Problem 16EQ

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