1) Suppose that you are a civil engineer working on a proposed change to a highway system. As part of an initial study you want to understand how traffic flow relates to distance from an airport. As part of the study you collected data as summarized below. Let d be the distance from an airport in km and s be the average speed of vehicles at that distance. You want to fit a polynomial p1 that describes s as a function of d by that polynomial. d s=f(d) 10 30 11 50 12 140 a) (3 points) Write the MATLAB code to fit the polynomial p1 of maximum degree possible for the data given b) (3 points) Plot the actual data and the polynomial p1 from a) on the same graph. c) (6 points) Using the model from part a, what will the predicted average speed at d = 11.5 km? d) (5 points) Use the model developed to predict the distance where the speeds is 75. 3) Generate data from the polynomial fit in part 1a) at points d= 10, 10.5, 11.2, 11.5. (6 points) Fit a polynomial p2 using a Newton Interpolating approach and a polynomial p3 using Lagrange interpolating polynomials. Each polynomial should be of the maximum possible degree that the data allows. Use MATLAB to plot the polynomials p2 and p3 on the same graph.