A BOD test was conducted on a wastewater. In the test, the sample was incubated for $3$ days at $20C$ and showed a $BO{D}_3$ of $286m\frac{g}{L}.$ If the rate constant $($base $e),k=0\mathrm{.}3d^{-1},$ the $BO{D}_5$ of the sample $($in units of $m\frac{g}{L})$ would be most nearly?

A$.1\mathrm{.}3{10}^2$

B$.1\mathrm{.}5{10}^2$

C$.2\mathrm{.}9{10}^2$

D$.3\mathrm{.}7{10}^2$

E$.4\mathrm{.}8{10}^2$

F$.7\mathrm{.}0{10}^2$

If a BOD test is conducted at $20C$ and a decay coefficient $($base e$)$ is determined to be $0\mathrm{.}20d^{-1},$ the value of the decay coefficient at $30C$ is expected to be most nearly?

A$.0\mathrm{.}20$

B$.0\mathrm{.}21$

C$.0\mathrm{.}35$

D$.1\mathrm{.}056$

E$.1\mathrm{.}135$

For a particular wastewater, the ultimate BOD was determined to be $3\mathrm{.}00{10}^{2}m\frac{g}{L}$ and the value of the decay coefficient $($base e$)$ was determined to be $0\mathrm{.}200d^{-1}$ at a temperature of $20C.$ If incubation is at $T=30C,$ the $BO{D}_5$ is expected to be most nearly?

A$.5\mathrm{.}34{10}^1$

B$.1\mathrm{.}10{10}^2$

C$.1\mathrm{.}90{10}^2$

D$.2\mathrm{.}47{10}^2$

E$.3\mathrm{.}00{10}^2$