A mass balance for a pollutant in a well-mixed lake can be written as (V)* dc/dt = W − Qc − kV √ c

(a) Given the parameter values V = 1 × 106 m3 , Q = 1 × 105 m3/yr, W = 1 × 106 g/yr, and k = 0.25 g0.5/m1.5/yr, use the Newton-Raphson method to solve for the steady-state concentration. Employ an initial guess of c0 = 4 g/m3 . Perform three iterations and determine εa after the third iteration.

(b) Repeat part 3a using the secant method. Let c0 = 4 and c1 = 6.

(c) Run the Matlab function massBalance. m to confirm your results for part 3a.

(d) Modify massBalance. m so that it implements the secant method (Hint: you will add another input variable, c1, to the first line of the program and then use this variable in your calculations).