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Calculating Concentration of Bacteria

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Please see the attached Word file and help answer the questions regarding concentration of bacteria in a water reservoir.

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Solution Summary

Using calculas, expression for concentration of bacteria in a water reservoir is estimated. Water with bacteria is continuously added in the reservoir and also being used by human society.

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Mass of bacteria added/time, k = 0.02*60000 = 1200 gm/day
Water in reservoir W = 400,000
At t =0, mass of bacteria in reservoir,
yo = 0.005*W = 0.005*400000 = 5*400 = 2000 gm

In dt time water added dW, such that,
r = dW/dt = 60,000 m^3/day

At t, mass of bacteria = y(t)
At t+dt, mass of bacteria,due to adding water:
y(t+dt) = y(t) + kdt

Total volume of water becomes = W + dW

Concentration of bacteria = (y(t) + kdt)/(W+dW)

same amount of water (dW) taken out of the reservoir in dt time, ...

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