$($a$)$ Determine the final BOD for a sample with an initial $5-$day BOD reading of $28m\frac{g}{L},$ given a decay rate of $\frac{0\mathrm{.}16}{?}$ day at $20C.(5$ points$)$

$($b$)$ Calculate the adjusted decay rate and the corresponding ultimate BOD when the sample temperature increases to $25C,$ assuming a temperature coefficient $()$ of $1\mathrm{.}072.$