Explanation Given information: If c and k are constants and Monod growth curve describes the growth of a population P, as a function of the available quantity of resources r, P = c r k + r . Formula used: Quotient rule of derivatives, ( f g ) ′ = f ′ ⋅ g − g ′ f g 2 Calculation: Consider the function P to calculate the population as below. P = c r k + r Since r is the independent variable. Thus, differentiate the equation P = c r k + r with respect to r. Use the quotient rule of derivatives ( f g ) ′ = f ′ ⋅ g − g ′ f g 2

Applied Calculus, 6e WileyPLUS + Loose-leaf

6th Edition

ISBN: 9781119408901

Author: Deborah Hughes-Hallett, Andrew M. Gleason, Patti Frazer Lock, Daniel E. Flath

Publisher: Wiley (WileyPLUS Products)

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Chapter 3.4, Problem 51P

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The derivative dPdr and interpretation of the result if c and k are constants and Monod growth curve describes the growth of a population P, as a function of the available quantity of resources r, P=crk+r.

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Chapter 3.4, Problem 50P

Chapter 3.4, Problem 52P

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Chapter 3 Solutions

Applied Calculus, 6e WileyPLUS + Loose-leaf

Ch. 3.1 - Prob. 1P Ch. 3.1 - Prob. 2P Ch. 3.1 - Prob. 3P Ch. 3.1 - Prob. 4P Ch. 3.1 - Prob. 5P Ch. 3.1 - Prob. 6P Ch. 3.1 - Prob. 7P Ch. 3.1 - Prob. 8P Ch. 3.1 - Prob. 9P Ch. 3.1 - Prob. 10P

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The derivative d P d r and interpretation of the result if c and k are constants and Monod growth curve describes the growth of a population P, as a function of the available quantity of resources r, P = c r k + r .

Solution Summary: The author explains how the derivative dP is inversely proportional to the square of resources available.

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To calculate:

The derivative dPdr and interpretation of the result if c and k are constants and Monod growth curve describes the growth of a population P, as a function of the available quantity of resources r, P=crk+r.

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Chapter 3 Solutions

The derivative d P d r and interpretation of the result if c and k are constants and Monod growth curve describes the growth of a population P, as a function of the available quantity of resources r, P = c r k + r .

Solution Summary: The author explains how the derivative dP is inversely proportional to the square of resources available.

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To calculate: The derivative dPdr and interpretation of the result if c and k are constants and Monod growth curve describes the growth of a population P, as a function of the available quantity of resources r, P=crk+r.

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Chapter 3 Solutions

To calculate:

The derivative dPdr and interpretation of the result if c and k are constants and Monod growth curve describes the growth of a population P, as a function of the available quantity of resources r, P=crk+r.