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A certain population is known to be growing at a rate given by the logistic equation = x(b – ax). Show that the maximum rate of growth will occur when the population is dx dt b equal to half its equilibrium size, that is, when the population is . 2a

A certain population is known to be growing at a rate given by the logistic equation = x(b – ax). Show that the maximum rate of growth will occur when the population is dx dt b equal to half its equilibrium size, that is, when the population is . 2a

Calculus: Early Transcendentals
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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A certain population is known to be growing at a rate given by the logistic equation dx x(b – ax). Show that the maximum rate of growth will occur when the population is dt b equal to half its equilibrium size, that is, when the population is 2a -
Transcribed Image Text:A certain population is known to be growing at a rate given by the logistic equation dx x(b – ax). Show that the maximum rate of growth will occur when the population is dt b equal to half its equilibrium size, that is, when the population is 2a -
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