$($Section $1\mathrm{.}9)$ Consider the discrete$-$time dynamical system modeling the concentration of a chemical in a lung. $($Note: round all

values at the end of the calculations and use $4$ decimal places.$)$

$c_{t+1}=(1-p)c_t+p$

Let $V=1\mathrm{.}5L,W=0\mathrm{.}4L,$ and $=2$mmo$\frac{l}{L}.$

If $c_0=6$mmo$\frac{l}{L},$ iterate to find the following values:

$c_1=$mmo$\frac{l}{L}$

$c_2=-$mmo$\frac{l}{L}$

$c_3=$mmo$\frac{l}{L}$

$c_4=$mmo$\frac{l}{L}$

Find the equilibrium of this system:

$c^{**}=$mmo$\frac{l}{L}$