Chapter 3, Exploration 2

Explore the dynamics of the linear system $x_{n+1}=m{x}_n+b$ 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.

2
0.2
0.020000000000000004
0.0020000000000000005
0.00020000000000000006
0.00002000000000000001
0.0000020000000000000008
2.000000000000001e-7
2.000000000000001e-8
2.000000000000001e-9
2.000000000000001e-10