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A population tries to grow exponentially but is limited by the resources of its environment. This growth is modeled by the differential equation dP k dt = -P(M-P). M Find a solution for this differential equation using the continuous growth rate k = 0.3, the carrying capacity M = 20, and the initial population size P(0) = 4. P(t) = Hint: You can solve the differential equation using separation of variables, but the calculations may be easier if you treat it as a Bernoulli equation.

A population tries to grow exponentially but is limited by the resources of its environment. This growth is modeled by the differential equation dP k dt = -P(M-P). M Find a solution for this differential equation using the continuous growth rate k = 0.3, the carrying capacity M = 20, and the initial population size P(0) = 4. P(t) = Hint: You can solve the differential equation using separation of variables, but the calculations may be easier if you treat it as a Bernoulli equation.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A population tries to grow exponentially but is limited by the resources of its environment. This growth is modeled by the differential equation dP k dt = -P(M-P). M Find a solution for this differential equation using the continuous growth rate k = 0.3, the carrying capacity M = 20, and the initial population size P(0) = 4. P(t) = Hint: You can solve the differential equation using separation of variables, but the calculations may be easier if you treat it as a Bernoulli equation.
Transcribed Image Text:A population tries to grow exponentially but is limited by the resources of its environment. This growth is modeled by the differential equation dP k dt = -P(M-P). M Find a solution for this differential equation using the continuous growth rate k = 0.3, the carrying capacity M = 20, and the initial population size P(0) = 4. P(t) = Hint: You can solve the differential equation using separation of variables, but the calculations may be easier if you treat it as a Bernoulli equation.
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