The farm in question plans on releasing a specific organic p

The farm in question plans on releasing a specific organic pollutant, called biphenyl, into the river. We have gathered some pertinent information regarding both the biphenyl and oxygen levels within the river near the release site. From our preliminary analysis, we know the farm will release biphenyl into the river at two possible rates (explained later). Once released, bacteria in the river will decomposé the biphenyl at a rate proportional to the amount of biphenyl present in the river. The natural decomposition of biphenyl is generally desirable, except that this process, called metabolic hydroxylation, also uses up the available oxygen in the river at the same rate as that at which biphenyl is decomposed. Additionally, the oxygen is replaced by diffusion from the air at the surface of the river at a rate proportional to the difference between the maximum oxygen level in the river xm and the current oxygen level

Solution

the amount of biphenyl in water will decrease as the bacteria that degrades biphenyl increases.

so

briver = breleased - breleased* no. of bacteria

diffusion of oxygen or amount of oxygen present in water (x) = xm - xo

where xm is maximum oxygen level and xo is the current oxygen level.

therefore the amount of biphenyl remaining in river (b) = breleased - breleased*no. of bacteria / t

and the amount of oxygen present (x) = xm-xo/ t