$(4$ pt$)$ ADR Equation

A wastewater treatment plant has been discharging treated effluent safely into a river.

However, because of heavy rain, untreated effluent containing chemical X was

discharged as overflow. A beach is located $10km$ downstream. How fast has chemical

$x$ been accumulating in the water at the beach?

Known parameters:

Dispersion coefficient $=10k\frac{m^2}{d}$

River average velocity $=0\mathrm{.}5k\frac{m}{d}$

$1$st order degradation, $r=-kC$;$k=0\mathrm{.}01d-1$

Concentration, $C,$ in $m\frac{g}{L}$ can be modelled by:

$C=2x^2+x+5,$ where $x$ is in $km$