Problem $6$: $(5$ points$)$

A BOD test is run using $50ml$ of treated wastewater mixed with $250ml$ of pure water. The initial DO of the mix is $10\mathrm{.}0m\frac{g}{L}($DO$(0)).$ After $5$ days, the DO is $3\mathrm{.}0m\frac{g}{L}($DO$(5$day$)).$ Assume that nitrification has been inhibited so that the only BOD being measured is carbonaceous.

$($a$)$ What is the $5-$day BOD?

$($b$)$ What is the remaining BOD after $5$ days?

$($c$)$ Estimate the reaction rate constant, $k?$ig k bh jn$$rt