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).

Calculus For The Life Sciences
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Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
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Chapter4: Calculating The Derivative
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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).
Compute the derivative: f'(x) = ______

Evaluate the derivative at the equilibrium: ___________

Is the equilibrium stable, unstable or neither? ________

 

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