Consider the reaction network:

$k_{0}A{k}_3$

$A{}_{k_2}^{k_1}B$

a$.$ Write the network topology for the system and the differential equations for all the species in the

system. $(2$ Point$)$

b$.$ Solve the differential equations to find the solutions for the system $($i$.$e$.,$ concentrations of A and

B $($i$.$e$.,a(t)$ and $b(t)$ in terms of state variables$).(5$ Points$)$

$($Hint: Consider utilizing the quasi$-$steady$-$state approximation for species involved in reactions

that occur much faster than others within the system. It's essential to thoroughly analyze all

reactions to determine which species maintain relatively constant concentrations over time.

Remember, it may not always be species A $($or B$!)$ that is in a quasi$-$steady state, so careful

assessment of each reaction is necessary to apply this approximation accurately$)$