The logistic curve is the graph of the function a f(x) = 1+ be-rx where a, b, and r are suitable parameters. This function may describe, for example, the initial rapid growth of a population, followed by a slowdown of the growth as resources become sparse. Since e¯™ª tends to zero as æ tends to infinity f(x) approaches a as æ tends to infinity, and at a = equals 0 the initial population a f(0) 1+b The rate r is the usual growth rate that would prevail indefinitely in the presence of unlimited resources. Suppose a = 4200, b = 10, and r = 0.01. Then the initial population is | and as time goes on the population approaches but never quite reaches
The logistic curve is the graph of the function a f(x) = 1+ be-rx where a, b, and r are suitable parameters. This function may describe, for example, the initial rapid growth of a population, followed by a slowdown of the growth as resources become sparse. Since e¯™ª tends to zero as æ tends to infinity f(x) approaches a as æ tends to infinity, and at a = equals 0 the initial population a f(0) 1+b The rate r is the usual growth rate that would prevail indefinitely in the presence of unlimited resources. Suppose a = 4200, b = 10, and r = 0.01. Then the initial population is | and as time goes on the population approaches but never quite reaches
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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Transcribed Image Text:The logistic curve is the graph of the function
a
f(x) =
1+ be-rx
where a, b, and r are suitable parameters.
describe, for example, the initial rapid growth of a population, followed
by a slowdown of the growth as resources become sparse. Since e¯™ tends to zero as a
This function
may
tends to infinity f(x) approaches .
equals
a as x tends to infinity, and at x =
0 the initial population
a
f(0) =
1+6
The rate r is the usual growth rate that would prevail indefinitely in the presence of
unlimited resources.
Suppose a = 4200, b = 10, and r = 0.01. Then the initial population is
and as time goes on the population approaches but never quite
reaches
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