A completely mixed lake with a single inflow and a single outflow stream has the following characteristics:

Mean depth = 5 m
Surface area = 11 * 106 m2
Residence time = 4.6 yr

An industrial plant presently discharges a chemical (W=2000 * 106 gr/yr) to the lake. In addition, the inflow stream also contains the same chemical at a concentration of 15 mg/L. Note that the volumetric inflow and outflow are equal. Assume that a first-order decay reaction can be used to characterize its removal by chemical oxidation. The reaction constant is k=0.1 yr-1.

a) Write a mass balance equation for this chemical
b) If the lake is at steady-state, compute the in-lake concentration of the chemical
c) If the lake is at steady-state, what industrial plant loading rate must be maintained to lower the lake's concentration to 30 ppm? Express your result as a percent reduction
d) Evaluate each of the following engineering options to determine which is the most effective for lowering the steady-state in-lake concentration of the chemical:

i) Reduce the present loading rate of the industrial plant by building a waste treatment facility that will remove 50% of the chemical from the plant's effluent
ii) Double the lake's depth by dredging
iii) Double the lake's outflow rate by diverting a chemical-free water as the second inflowing stream to the lake

e) Determine the 95% response times for each of the alternative options given in part (d).