$13-13$ For two equal$-$sized, well$-$mixed tanks arranged in series, $E(t)=4\frac{t}{\frac{?}{?}}$bar $(t{)}^2{e}^{-2\frac{t}{\frac{?}{?}}\text{b}\text{a}\text{r}(t)}.$

$($a$)$ Develop the expressions for $F(t)$ and $W(t)$ for this system.

$($b$)$ What is the value of $F(t)$ at $t=5$min, when the mean residence time $($i$)$ is $10$min $?$