1. Pollutant X is found in a lake (with ~50 km water) besides a city. The lake receives water input from inflowing stream (a river), which contributes Q m3/day water. However, this input doesn't change the lake water volume much since some of the lake water loses to groundwater and the air. X is found in the inflowing stream (the river) to be 0.01 g/m, steady everyday, but is not found in the air or groundwater. X can be consumed by a kind of fish in the lake following a first-order decay: change of concentration (c) due to fish: = -0.005c. in g/m/day (a) Build a one-box model for the pollutant X in this lake. Write down the continuity equation =?) dc dt dt (b) The concentration of X in the lake is measured to be 0.02 g/m, steady everyday. What is the average stream flow from the water (Q = ?) (c) At one day, a factory was open near the lake and released X to the lake at the rate of 50 kg/day. Rewrite the continuity equation by adding this emission and the calculated value of Q in (b). (d) With the initial concentration of X, Co = 0.02 g/m?, what is the concentration after 30 days? Please give the exact (analytical) solution. (e) Solve (d) again numerically with the forward Euler scheme. Use a timestep of 10 days. (f) What's the error of this numerical solution in (e)? Is the method stable? Why