a$)$ Prove that the decay constant $(k)$ in Horton's infiltration equation can be expressed as follows: $k=\frac{f_0-f_c}{F_c}$; where $F_c$ is the area under the infiltration curve $f(t)$ and $f(t)=f_c,f_0$ and $f_c$ are the infiltration rates at $t=0$ and $t=$ infinity respectively.