$3.$ A $15-$ml sample is pipetted directly into a $300-$ml incubation bottle. The initial DO of$$ the diluted sample is $8\mathrm{.}4$mg$/$L$,$ and its final DO after the $5-$day test is $1\mathrm{.}8$ mg$/$L$.$ The seeded dilution water is separately incubated in a $300-$ml bottle for $5$ days, and the initial and financial D$$ concentrations are respectively $8\mathrm{.}8$ mg$/$L and $7\mathrm{.}5$mg$/$L$.$ After a long period of time, the sample DO is $0\mathrm{.}5$m g$/$L$,$ and it no longer seems to be dropping. The dilution water DO is reduced to $7\mathrm{.}0$ mg$/$L$.$ Assurn e nitrification has been inhibited so the only BOD measured is carbonaceous.

a$.$ If the same and the seeded dilution water are both incubated at $20$ degC for$5$ days, what is the BOD$$ of the sample

b$.$ Assuming no nitrification effects, estimate the ultimate carbonaceous BOD$($L$)$

c$.$ What would be the remaining BOD after $5$ days have elapsed $($L$)$

d$.$ Estimate the deaeration reaction rate constant k$($day$)$