The table below summarizes rainfall data for a storm event in a $50-$acre watershed in

Corpus Christi, TX$.$ The total runoff during the storm was $100,000f{t}^3.$ The watershed

soil is capable of infiltrating at a rate of $2\mathrm{.}0i\frac{n}{h}r$ at the beginning of the storm. By

the end of the storm, it can only infiltrate at $\frac{1}{3}$ of the initial rate. Assume the decay

constant is $0\mathrm{.}33h{r}^{-1}.$

$($a$)$ Use the $$ index method to find the total infiltration during the storm event $($in

inches$).$

$($b$)$ Use Horton's method to find the time $($after the start of the storm$)$ when the

infiltration rate is approximately half of the initial rate.

$($c$)$ Use Horton's method to find the total infiltration during the storm event $($in

inches$).$

$($d$)$ How do the methods from parts $($a$)$ and $($c$)$ differ? Which do you think is a more

accurate estimate of actual infiltration during the storm? Why?