Exercise $5\mathrm{.}2\mathrm{.}4$ In this model, let $r=4,$ and assume that the initial value is $x_0=0\mathrm{.}6.$ Simulate the model in two different ways:

a$)$ Use SageMath to print the values of $x_0,x_1,x_2,$dots, up to at least $x_{20}.$

b$)$ With the help of a simple pocket calculator $($or a calculator app on your phone$),$ create the same list on paper. In this case, continue until the numbers that you are calculating on paper look completely different from the numbers that SageMath gave you.