Code in R

Solution of the difference equation $x_n=r{x}_{n-1}(1-x_{n-1}),$ with starting value x $1.($a$)$ Write a function

quadmap$($ start, rho, niter $)$ which returns the vector $(x_1,$dots,$x_n)$ where $x_k=r{x}_{k-1}(1-x_{k-1})$ and niter

denotes n $,$ start denotes x $1,$ and rho denotes r $.$

Try out the function you have written: for $r=2$ and $x_{n}0\mathrm{.}5n0$ you should get $x_{n}0\mathrm{.}5asn.$

Try quadmap$(start=0\mathrm{.}95,$ rho$=2\mathrm{.}99,$ niter$=500)$ Now type this into the Console: plot$(tmp,$

type$="l")$ Also try plot$(tmp[300$:$500],$ type$="l")$