219k views
3 votes
Consider the recursive relation xₜ₊₁=2xₜ e ⁻ˣₜ(a) Find all equilibrium points. Answer: x= and x=

(b) The smaller equilibrium is
(c) The larger equilibrium is
(d) On your own, draw the function f(x) and perform cobwebbing. (No need to upload anything here.)

1 Answer

3 votes

Final answer:

The recursive relation xₜ₊₁=2xₜ e ⁻ˣₜ has two equilibrium points: x = 0 and x = 1. To draw the function f(x) and perform cobwebbing, plot the graph of the function and visually represent the recursive relation by drawing lines connecting points on the graph.

Step-by-step explanation:

The recursive relation is given by xₜ₊₁=2xₜ e ⁻ˣₜ.

(a) To find the equilibrium points, we need to solve the equation xₜ₊₁ = xₜ, which leads to:
x = 2x e ⁻ˣ.

(b) The smaller equilibrium is x = 0.

(c) The larger equilibrium is x = 1.

(d) To draw the function f(x) and perform cobwebbing, you can plot the graph using software or manually draw it. Cobwebbing involves visually representing the recursive relation on the graph by drawing lines connecting points on the graph.

User Knutin
by
7.1k points