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Logistic population growth Widely used models for popula- tion growth involve the logistic equation P'(t) = rP( K where P(t) is the population, for t > 0, and r > 0 and K > 0 are given constants. a. Verify by substitution that the general solution of the equation K is P(t) 1+ Cei• where C'is an arbitrary constant. b. Find the value of C that corresponds to the initial condition P(0) = 50. c. Graph the solution for P(0) = 50, r = 0.1, and K = 300. d. Find lim P(t) and check that the result is consistent with the graph in part (c).

Logistic population growth Widely used models for popula- tion growth involve the logistic equation P'(t) = rP( K where P(t) is the population, for t > 0, and r > 0 and K > 0 are given constants. a. Verify by substitution that the general solution of the equation K is P(t) 1+ Cei• where C'is an arbitrary constant. b. Find the value of C that corresponds to the initial condition P(0) = 50. c. Graph the solution for P(0) = 50, r = 0.1, and K = 300. d. Find lim P(t) and check that the result is consistent with the graph in part (c).

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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Logistic population growth Widely used models for popula- tion growth involve the logistic equation P'(t) = rP( K where P(t) is the population, for t > 0, and r > 0 and K > 0 are given constants. a. Verify by substitution that the general solution of the equation K is P(t) 1+ Cei• where C'is an arbitrary constant. b. Find the value of C that corresponds to the initial condition P(0) = 50. c. Graph the solution for P(0) = 50, r = 0.1, and K = 300. d. Find lim P(t) and check that the result is consistent with the graph in part (c).
Transcribed Image Text:Logistic population growth Widely used models for popula- tion growth involve the logistic equation P'(t) = rP( K where P(t) is the population, for t > 0, and r > 0 and K > 0 are given constants. a. Verify by substitution that the general solution of the equation K is P(t) 1+ Cei• where C'is an arbitrary constant. b. Find the value of C that corresponds to the initial condition P(0) = 50. c. Graph the solution for P(0) = 50, r = 0.1, and K = 300. d. Find lim P(t) and check that the result is consistent with the graph in part (c).
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