Using Horton's Infiltration Capacity model, and assuming f$,5$ in$/$hr$,$ fc $0\mathrm{.}15$ in$/$hr and k$=0\mathrm{.}8/$hr$.$

a$)$ Determine the infiltration rate, in$/$hr$,15$ and $30$ minutes from the start of rainfall.

b$)$

Determine the amount of infiltration, inches, that can occur during the first $30$ minutes.

c$)$ For a rainfall amount of $2\mathrm{.}25$ inches in the first $30$ minutes, determine the amount of runoff, in inches. You may ignore interception and puddle storage losses.

d$)$ In part c$),$ what if the rainfall were only $1\mathrm{.}5$ inches, how much runoff would occur?