In the study of population dynamics one of the most famous models for a growing but bounded population is the logistic equation dP = P(a - bP), where a and are positive constants. Although we will come back to this equation and solve it by an alternative method in Section 3.2, solve the DE this first time using the fact that it is a Bernoulli equation. P(t) =

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 9T
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In the study of population dynamics one of the most famous models for a growing but bounded population is the logistic equation
dP
%3D Р(а — БР),
dt
-
where a and b are positive constants. Although we will come back to this equation and solve it by an alternative method in Section 3.2, solve the DE this first time using the fact that it is a Bernoulli equation.
P(t)
Transcribed Image Text:In the study of population dynamics one of the most famous models for a growing but bounded population is the logistic equation dP %3D Р(а — БР), dt - where a and b are positive constants. Although we will come back to this equation and solve it by an alternative method in Section 3.2, solve the DE this first time using the fact that it is a Bernoulli equation. P(t)
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