For a condition where infiltration rate is less than rainfall intensity (ponding occurs), write a few lines of Matlab code to use Newton's method to solve the cumulative infiltration equation (F.): YAO + F F = F-1 + YA0 In + K-At Note that the solution of F; using Newton's method is done through iteration (4 iterations should be sufficient to provide an adequate answer) and you will thus have to use a FOR loop in Matlab. The general format of the Newton's equation for this case is: g(Fem) Fen+1 = Fen g(Fen) Test your Matlab code by using the following parameters and values: Assume a Loamy Sand soil (Table 2) Time step = 15 minutes S, = 0.45 and Ae = (1 S)e, (see class notes for details ) Use F-1 = 1 cm as your input cumulative infiltration value from the previous time period. You can also use this same value as the starting point for your Newton's method iteration. In your assignment: Give the function g(F,) that you are finding a root for using Newton's method. Give the derivative g'(F.) of the function g(F) that you are finding a root for using Newton's method. Provide the value for F, as specified above.