The question of whether an optimal body size exists for different kinds of animals is one that is of great interest to biologists. The reproductive power P of an individual can be modeled, following the ideas of ecologist James H. Brown (see his book Macroecology, University of Chicago Press, 1995), as the harmonic mean of two limiting rates. The harmonic mean of two numbers a and b is the reciprocals of the average of the inverses of the two numbers: = ti The two rates are a per-unit-mass rate R1 at which individuals acquire resources, and a per-unit-mass rate R2 at which individuals convert those resources into new individuals; that is, RR2 P= Ri+R2 Assuming both Rị and R2 are the following allometric functions of body mass measure in kilograms R1 2M3/4 and R2 = 4M-1/4, find the body mass M that maximizes the reproductive power P, М- kg.

The question of whether an optimal body size exists for different kinds of animals is one that is of great interest to biologists. The reproductive power P of an individual can be modeled, following the ideas of ecologist James H. Brown (see his book Macroecology, University of Chicago Press, 1995), as the harmonic mean of two limiting rates. The harmonic mean of two numbers a and b is the reciprocals of the average of the inverses of the two numbers: = ti The two rates are a per-unit-mass rate R1 at which individuals acquire resources, and a per-unit-mass rate R2 at which individuals convert those resources into new individuals; that is, RR2 P= Ri+R2 Assuming both Rị and R2 are the following allometric functions of body mass measure in kilograms R1 2M3/4 and R2 = 4M-1/4, find the body mass M that maximizes the reproductive power P, М- kg.

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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