Suppose that the population x, of bacteria satisfies the discrete time dynamical system X1 where r is a parameter, and 0

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter5: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 5CC
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X1+1=
Suppose that the population x, of bacteria satisfies the discrete time dynamical system
Xt
where r is a parameter, and 0 <r < 1.
r+ (x₂)²
If x = 0, what is X₁+1?
Is x* = 0 an equilibrium?
If x₁ = √√/1-7, what is X₁+1 ?
Is x* = √√/1-r an equilibrium?
Write the updating function rule as f(x) =
Compute the derivative: f'(x) =
x* = √1-r is stable?
C
What condition on guarantees that the equilibrium
Transcribed Image Text:X1+1= Suppose that the population x, of bacteria satisfies the discrete time dynamical system Xt where r is a parameter, and 0 <r < 1. r+ (x₂)² If x = 0, what is X₁+1? Is x* = 0 an equilibrium? If x₁ = √√/1-7, what is X₁+1 ? Is x* = √√/1-r an equilibrium? Write the updating function rule as f(x) = Compute the derivative: f'(x) = x* = √1-r is stable? C What condition on guarantees that the equilibrium
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