Suppose there is a population of rabbits that (when left alone) experiences population growth at a rate proportional (with k = o when the population is measured in thousands and time in years) to the product of the difference between the current population and the threshold population and the difference between the carrying capacity and the current population. %3D Assume that the threshold population is 1 thousand and the carrying capacity is 8 thousand. Further suppose that predators eat an amount of these rabbits proportional (with k = when the population is measured in thousands and time in years) to the current rabbit population. (a) Write down a differential equation that models this population of rabbits P in thousands based on the time t in years. (b) Find all equilibrium solutions to this differential equation. (c) Suppose the initial population of rabbits is 5 thousand. Determine the long term behavior for this rabbit population.
Suppose there is a population of rabbits that (when left alone) experiences population growth at a rate proportional (with k = o when the population is measured in thousands and time in years) to the product of the difference between the current population and the threshold population and the difference between the carrying capacity and the current population. %3D Assume that the threshold population is 1 thousand and the carrying capacity is 8 thousand. Further suppose that predators eat an amount of these rabbits proportional (with k = when the population is measured in thousands and time in years) to the current rabbit population. (a) Write down a differential equation that models this population of rabbits P in thousands based on the time t in years. (b) Find all equilibrium solutions to this differential equation. (c) Suppose the initial population of rabbits is 5 thousand. Determine the long term behavior for this rabbit population.
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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PLEASE do this asap and show all of your step by step please. thank you so much.
Transcribed Image Text:Suppose there is a population of rabbits that (when left alone) experiences population growth at a
rate proportional (with k = to when the population is measured in thousands and time in years)
to the product of the difference between the current population and the threshold population and
the difference between the carrying capacity and the current population.
Assume that the threshold population is 1 thousand and the carrying capacity is 8 thousand.
Further suppose that predators eat an amount of these rabbits proportional (with k = when
the population is measured in thousands and time in years) to the current rabbit population.
(a) Write down a differential equation that models this population of rabbits P in thousands
based on the time t in years.
(b) Find all equilibrium solutions to this differential equation.
(c) Suppose the initial population of rabbits is 5 thousand. Determine the long term behavior
for this rabbit population.
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