a$)$ Simulate the system from initial conditions $($in mM$)($s$1,$ s$2,$ s$3)=(0\mathrm{.}3,0\mathrm{.}2,0\mathrm{.}1).$ Repeat with initial condition $($s$1,$ s$2,$ s$3)=(6,4,4).$

b$)$ Generate an approximate model in which the rates of reactions $1,2,$ and $3$ follow first$-$order mass$-$action kinetics $($i$.$e$.$ vi $=$ kisi, for i $=1,2,3).$ Choose values for the rate constants ki that give a good approximation to the original nonlinear model. Explain your reasoning. $($Hint: Exercise $3\mathrm{.}1\mathrm{.}2($b$)$ provides one viable approach.$)$

c$)$ Simulate your simpler $($mass$-$action based$)$ model from the sets of initial conditions in part $($a$).$ Comment on the fit. If the approximation is better in one case than the other, explain why.