Consider a $120-$min storm event with a total rainfall amount of $80$ mm$.$ With a decay constant k in Horton$$s

infiltration model of $0\mathrm{.}00833$ min$-1$ and knowing that the initial and ultimate infiltration rates are $30$ mm$/$h and

$2$ mm$/$h$,$ respectively:

a$)$ Determine the Potential Infiltration Rate in mm$/$hr

b$)$ Determine the Cumulative Infiltration Capacity in mm$.$