Consider a reactor modeled as \(N\) interconnected tanks in series. Derive an expression for the exit response for a bolus injection of a tracer.

Show that the maximum value of the tracer concentration is given by the following expression:

\[C_{\max }=\frac{N(N-1)^{N-1}}{(N-1) !} \exp [-(N-1)]\]

and this occurs at a dimensionless time of \((N-1) / N\).