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Growth rates for many microbes and plants depend on the amount of nutrients that are available to them. Monod introduced a model, now widely adopted, for how the rate of growth of E.coli bacteria depends on the level of glucose in the medium in which the bacteria are grown. Specifically, Monod observed that the reproduction rate of the bacteria (number of cell divisions in one hour) is given as a function of the glucose concentration (C, measured in units of mM) by the following equation. Is r(C) an increasing function of C? C C+0.022 r(C)= 13.5- C>0 Choose the correct answer below. A. r(C) is not an increasing function of C because r'(C)= B. (C) is an increasing function of C because r'(C)= O c. r(C) is not an increasing function of C because r''(C) = O D. r(C) is an increasing function of C because r''(C): 0.297 (C+0.022)² 0.297 (C+0.022)² 0.594 (C+0.022) ³ 0.594 (C+0.022)³ therefore r'(C) <0 for C> 0. therefore r'(C) > 0 for C > 0. therefore r''(C) <0 for C> 0. therefore r''(C) > 0 for C> 0.

Growth rates for many microbes and plants depend on the amount of nutrients that are available to them. Monod introduced a model, now widely adopted, for how the rate of growth of E.coli bacteria depends on the level of glucose in the medium in which the bacteria are grown. Specifically, Monod observed that the reproduction rate of the bacteria (number of cell divisions in one hour) is given as a function of the glucose concentration (C, measured in units of mM) by the following equation. Is r(C) an increasing function of C? C C+0.022 r(C)= 13.5- C>0 Choose the correct answer below. A. r(C) is not an increasing function of C because r'(C)= B. (C) is an increasing function of C because r'(C)= O c. r(C) is not an increasing function of C because r''(C) = O D. r(C) is an increasing function of C because r''(C): 0.297 (C+0.022)² 0.297 (C+0.022)² 0.594 (C+0.022) ³ 0.594 (C+0.022)³ therefore r'(C) <0 for C> 0. therefore r'(C) > 0 for C > 0. therefore r''(C) <0 for C> 0. therefore r''(C) > 0 for C> 0.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Growth rates for many microbes and plants depend on the amount of nutrients that are available to them. Monod introduced a model, now widely adopted, for how the rate of growth of E.coli bacteria depends on the level of glucose in the medium in which the bacteria are grown. Specifically, Monod observed that the reproduction rate of the bacteria (number of cell divisions in one hour) is given as a function of the glucose concentration (C, measured in units of mM) by the following equation. Is r(C) an increasing function of C? C C + 0.022 r(C) = 13.5- C>0 Choose the correct answer below. O A. r(C) is not an increasing function of C because r' r'(C)= B. r(C) is an increasing function of C because r'(C) = O c. r(C) is not an increasing function of C because r''(C) = D. r(C) is an increasing function of C because r''(C) = 0.297 (C+0.022)² 0.297 (C+0.022)² " therefore r' (C) <0 for C > 0. 0.594 (C+0.022)³ therefore r' (C) > 0 for C > 0. 0.594 3' (C+0.022) ³¹ therefore r''(C) <0 for C > 0. therefore r''(C) > 0 for C> 0.
Transcribed Image Text:Growth rates for many microbes and plants depend on the amount of nutrients that are available to them. Monod introduced a model, now widely adopted, for how the rate of growth of E.coli bacteria depends on the level of glucose in the medium in which the bacteria are grown. Specifically, Monod observed that the reproduction rate of the bacteria (number of cell divisions in one hour) is given as a function of the glucose concentration (C, measured in units of mM) by the following equation. Is r(C) an increasing function of C? C C + 0.022 r(C) = 13.5- C>0 Choose the correct answer below. O A. r(C) is not an increasing function of C because r' r'(C)= B. r(C) is an increasing function of C because r'(C) = O c. r(C) is not an increasing function of C because r''(C) = D. r(C) is an increasing function of C because r''(C) = 0.297 (C+0.022)² 0.297 (C+0.022)² " therefore r' (C) <0 for C > 0. 0.594 (C+0.022)³ therefore r' (C) > 0 for C > 0. 0.594 3' (C+0.022) ³¹ therefore r''(C) <0 for C > 0. therefore r''(C) > 0 for C> 0.
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