A chemostat dynamics, as shown by Fig. $1,$ using Michaelis$-$Menten Kinetics is given by the following equations:

Figure $1.$ A chemostat diagram featuring inflow $($nutrient support$)$ and outflow $($disposal$).$

TASKS

$1.$ A scientist sets up a chemostat experiment which is governed by Eq$.(4)$ and $(5).$ The scientist experimentally learned the constants and initial conditions as given in Table $1$ for each project group.

$($a$)$ Simulate this system and plot the variables N$($t$)$ and C$($t$)$ of the experiment versus time t$.$ N$0=14\mathrm{.}73$ C$0=4\mathrm{.}96$