Answer part 2 please P' = rPaKwhere 0 < a< K and r is a positive constant. Identify all equilibrium populations and determine the stability ofeach equilibrium.Reach: Given a group of animals that grows according to this model and begins with members, what can yousay about the long term prospects of the animal population, if anything? Does the situation change if you beginwith 2K animals? Explain your answers.

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Answered: Reach: Given a group of animals that…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter7: Exponents And Exponential Functions

Section7.8: Transforming Exponential Expressions

Problem 12PFA

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Population equilibria can be stable or unstable. If, when a population deviates a bit from the equilibrium value (as populations inevitably do), it tends to return to it, this is a stable equilibrium; if, however, when the population deviates from the equilibrium it tends to diverge from it even further, this is an unstable equilibrium. Think of a ball in the pocket of a snooker table versus a ball balanced on a snooker cue. Unstable equilibria are a feature of Allee effect models such as the following. dN Use a phase portrait of the autonomous equation above to determine whether the nonzero equilibria that you found in question (2) are stable or unstable. (Hint: See Section 2.1 of the text. List the equilibria according to their stability. Enter your answers as comma-separated lists. If there are no equilibria in a certain category, enter NONE.) stable N = unstable N =
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Reach: Given a group of animals that grows according to this model and begins with members, what can you say about the long term prospects of the animal population, if anything? Does the situation change if you begin with 2K animals? Explain your answers.