A small lake with volume of 20,000 m^3 has no natural pollutant sources. However, a sewage pipe discharges sewage containing an organic polluntant into the lake. Conditions in the sewage pipe are Qs= 0.5 m^3/s, and Cs= 100mg/L. The pollutant is destroyed in the lake with a first-order rate constant of 0.2/d. The flow rate out of the lake is 5.0 m^3/s. Assume that the lake is well mixed.
(a) Calculate the steady-state pollutant concentration in the lake and
(b) what is the retention time for this lake?