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The scientists Verhulst (1828) and Peal (1930) proposed the following growth model for a population living in an environment with limited resources (e.g. space, food, sunlight, etc):
= ,
where is the natural growth rate of the population when resources are limited and is a positive constant called carrying capacity of the environment.
(a) Using sign analysis, find all constant solution and discuss the general behavior of solution.
(b) Solve the equation when Compute the limit as of your solution.
(c) Solve the equation when Compute the limit as of your solution.
(d) Discuss why is called carrying capacity.
. Model : Logistic Model I
Differential Equation :
General Solution :
Graph :

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