A population model is used to describe how the rate of reproduction of organisms depends on the amount of nutrients that are available. The model shows how the rateof division of E. coli cells depends upon the amount of sugar added to their growth flask. If r is the rate of reproduction (number of divisions in one hour) and C is theamount of glucose sugar added to the growth medium measured in moles, then the following applies.1.35Cr(C) =-4C+0.27 x 10 (a) Show that the reproduction rate goes to zero when the sugar level is low; that is lim r(C) = 0.C→01.35 ()Since r is continuous at C = 0, lim r(C) =r(|= 0.4+ 0.27 x 10C-0

r(C)=1.35CC+0.27×10-4Substitute C=0r(0)=1.35(0)0+0.27×10-4r(0)=0

Answered: (a) Show that the reproduction rate…

(a) Show that the reproduction rate goes to zero when the sugar level is low; that is lim r(C)= 0. C→0 1.35 Since r is continuous at C= 0, lim r(C)= r(| = 0. - 4 + 0.27 x 10 C→0

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 91E

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Question

A population model is used to describe how the rate of reproduction of organisms depends on the amount of nutrients that are available. The model shows how the rate
of division of E. coli cells depends upon the amount of sugar added to their growth flask. If r is the rate of reproduction (number of divisions in one hour) and C is the
amount of glucose sugar added to the growth medium measured in moles, then the following applies.
1.35C
r(C) =
-4
C+0.27 x 10

(a) Show that the reproduction rate goes to zero when the sugar level is low; that is lim r(C) = 0.
C→0
1.35 ()
Since r is continuous at C = 0, lim r(C) =r(|
= 0.
4
+ 0.27 x 10
C-0

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