$f(t)=f_c+(f_0-f_c)e^{(-kxt)}$

Suppose the infiltration of water into a certain type of soil can be described by Horton's equation with the following parameters: initial infiltration rate, $fo,=50m\frac{m}{h}$; ultimate infiltration rate, $fc=10m\frac{m}{h}$; and decay constant $=4h^{-1}.$

$($a$)$ Determine the infiltration rate and cumulative infiltration at $1hr$ increments up to $3hr$ from the beginning of infiltration. Assume continuous ponding. $(9$ points$)$

$($b$)$ What is the total infiltration amount after $3$ hours $(2$ points$).$