For a small catchment,

a$)$ the infiltration capacity is represented by Horton's equation as

$f_p=0\mathrm{.}5+1\mathrm{.}2e^{-0\mathrm{.}5t}$

where $f_p$ is in $c\frac{m}{h}$ and $$ is in hours. Assuming the infiltration to take place at capacity rates in a storm of $4$ hours duration, estimate the average rate of infiltration for the duration of the storm.

b$)$the infiltration rate was observed to be $10c\frac{m}{h}$ at the beginning of the rain and it decreased exponentially to an equilibrium value of $1\mathrm{.}0c\frac{m}{h}$ at the end of $9$ hours of rain. If a total of $18cm$ of water infiltered during $9$ hours interval, find the value of the decay constant $(K_h)$ in Horton's infiltration equation.