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The single species Gompertz population model was first proposed by Benjamin Gompertz in 1825 and has been used widely to model the population growth of the human. The equation is given by K dP rP ln| dt P(0) = P, where P(t)is defined to be the population of the human at time, t, ris the population growth rate and K is the carrying capacity of the environment. i) Solve the Gompertz equation by using separable method. ii) Use the solution obtained in i) to compute the population of the human at time t= 5,10 and 20 years if K = 200, r =0.02 and P(0)=50. Interpret the result.

The single species Gompertz population model was first proposed by Benjamin Gompertz in 1825 and has been used widely to model the population growth of the human. The equation is given by K dP rP ln| dt P(0) = P, where P(t)is defined to be the population of the human at time, t, ris the population growth rate and K is the carrying capacity of the environment. i) Solve the Gompertz equation by using separable method. ii) Use the solution obtained in i) to compute the population of the human at time t= 5,10 and 20 years if K = 200, r =0.02 and P(0)=50. Interpret the result.

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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The single species Gompertz population model was first proposed by Benjamin Gompertz in 1825 and has been used widely to model the population growth of the human. The equation is given by K = rP ln| P dP P(0) = P, dt where P(t)is defined to be the population of the human at time, t, ris the population growth rate and K is the carrying capacity of the environment. i) Solve the Gompertz equation by using separable method. ii) Use the solution obtained in i) to compute the population of the human at time t = 5,10 and 20 years if K = 200, r= 0.02 and P(0)=50. Interpret the result.
Transcribed Image Text:The single species Gompertz population model was first proposed by Benjamin Gompertz in 1825 and has been used widely to model the population growth of the human. The equation is given by K = rP ln| P dP P(0) = P, dt where P(t)is defined to be the population of the human at time, t, ris the population growth rate and K is the carrying capacity of the environment. i) Solve the Gompertz equation by using separable method. ii) Use the solution obtained in i) to compute the population of the human at time t = 5,10 and 20 years if K = 200, r= 0.02 and P(0)=50. Interpret the result.
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