$($a$)$ Using the Streeter$-$Phelps equation, draw the DO sag curve for the following conditions: $k_d=0\mathrm{.}042d^{-1}$;$k_{La}=0\mathrm{.}29d^{-1}$;$L_0=75m\frac{g}{L}$;$DO($saturated$)=9\mathrm{.}2m\frac{g}{L}$;$DO($initial$)=5\mathrm{.}7m\frac{g}{L}$; flow velocity $=9\mathrm{.}5k\frac{m}{d}.$

$($b$)$ Determine the location $($time$)$ of the critical point. What is the DO concentration at the critical point? Do you expect a healthy aquatic ecosystem near the critical point of the river?

$($c$)$ How long does it take until DO recovers above $4mg-\frac{O_2}{L}?$