Past exam of the topics in applied mathematics course of the University of Oxford / 2007 / A / 2 / ii / Solution

Adding the last two equations gives $d(e+c)/dt=0$. The initial conditions therefore imply $\boxed{e+c=e_0}$, or $e=e_0-c$. Substitute this in the first two balances:The enzyme inventory is conserved even while substrate can grow autocatalytically.