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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.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 18T
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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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