Consider the discrete-time dynamical system xt+1 = 5xt(1-xt). If xt = 4/5, xt +1 = _____ Is x1 = 4/5 an equilibrium for this system? ______ Write the updating function rule as f(x) = 5x(1-x).

Consider the discrete-time dynamical system xt+1 = 5xt(1-xt). If xt = 4/5, xt +1 = _ Is x1 = 4/5 an equilibrium for this system? __ Write the updating function rule as f(x) = 5x(1-x).

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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Question

Consider the discrete-time dynamical system x_t+1= 5x_t(1-x_t).
If x_t = 4/5, x_t +1 = _____
Is x₁ = 4/5 an equilibrium for this system? ______
Write the updating function rule as f(x) = 5x(1-x).
Compute the derivative: f'(x) = ______

Evaluate the derivative at the equilibrium: ___________

Is the equilibrium stable, unstable or neither? ________