Chapter 3, Exploration 2

Explore the dynamics of the linear system \(x_{n+1} = mx_n +b\) when \(b = 0\). You should pay particular attention to how chaniging the value of \(m\) with the slider affects the fixed point and/or its stability. The initial condition for this tool is \(x=2\). There are three views available. You can select a table of the system, a plot of the points in the sequence with \(n\) on the horizontal axis, or a stairstep diagram.

Describe what you see.