(USE MATLAB FOR PART C AND D!) A mass balance for a pollutant in a well-mixed lake can be written as V(dc/dt_=WQckVc

(a) Given the parameter values V= 110^6 m^3,Q= 110^5 m^3/yr, W= 110^6 g/yr, and k= 0.25 m^0.5/g^0.5/yr, use the Newton-Raphson method to solve for the steady-state concentration. Employ an initial guess of c= 4 g/m^3. Perform three iterations and determine a after the third iteration.

(b) Repeat part 3a using the modified secant method

x_i+1=xi[(xi f(xi))/(f(xi+xi)f(xi))]. Let = 0.5.

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

(d) Modify massBalance.m so that it implements the modified secant method