In C$++$ please:

Write a computer program to solve the following non$-$linear difference equation: x$($t$+1)=$ rx$($t$)(1-$x$($t$))$ for the following values of r and x$(0)$:

$($a$)$ x$(0)=0\mathrm{.}5,$ r$=1\mathrm{.}2$; $($b$)$ x$(0)=0\mathrm{.}5,$ r$=0\mathrm{.}1$; $($c$)$ x$(0)=0\mathrm{.}1,$ r$=2\mathrm{.}8$; $($d$)$ x$(0)=0\mathrm{.}5,$ r$=2\mathrm{.}8$; $($e$)$ x$(0)=0\mathrm{.}1,$ r$=3\mathrm{.}0$; $($f$)$

x$(0)=0\mathrm{.}5,$ r$=3\mathrm{.}0$; $($g$)$ x$(0)=0\mathrm{.}1,$ r$=3\mathrm{.}10$; $($h$)$ x$(0)=0\mathrm{.}1,$ r$=3\mathrm{.}6$; $($i$)$ x$(0)=0\mathrm{.}1,$ r$=3\mathrm{.}8$; $($j$)$ x$(0)=0\mathrm{.}1,$ r$=3\mathrm{.}9$; $($k$)$

x$(0)=0\mathrm{.}1,$ r$=4\mathrm{.}0$

Plot x$($t$+1)$ vs$.$ x$($t$)$ for each of these cases. Try to interpret the results. Are they strange? $[$This exercise is to illustrate the so called Chaos$]$

Note: You solve the equation using C$++$ and Excel $($or Simlab or another program to plot x$($t$+1)$ vs$,$ x$($t$)$