Question 1: Consider a small lake hydraulic behavior of which can be represented by a complete mix flow reactor. It is known that an organic contaminant is being continuously discharged into this lake with a constant load of 15.5 kg/h and at the 15th day of discharge, contaminant concentration in the lake is 12 mg/L. It is also known that the degradation kinetics of this organic contaminant follows a second-order kinetics. The surface area of the lake is 100 ha and it has an average depth of 2.5 m. Take the degradation rate constant as 5x10-6 L/mg/h. You can assume no additional inflow of this contaminant into the lake through groundwater flow etc., and a total of 500 m /h of water is also abstracted from the lake for human use. a) Write the mathematical model equation and the relevant (initial and inlet) conditions that can be used to predict the concentration of the organic contaminant in the above described lake system. .