[10pts] Problem #1) The data below shows the percentage of Ph.D. students and the time between their initial proposal and dissertation defense. Table I. Time required for Ph.D. students to defend their dissertation Time since proposal (yrs) 1.6 2.0 2.5 3.2 4.0 4.5 Percentage of Ph.D. students (%) 14 15 a) Write a MATLAB code to estimate the percentage of graduate students who take 2.8 years to defend their dissertation (i.c. f (2.8)). Use Newton polynomials of order 1 through 3 to calculate the values. Choose the sequence of the points to attain the best possible accuracy. b) For the 3t order Newton polynomial, write out the error expression Rs (no need to solve). c) Verify your answers from part a) by hand calculation. d) Repeat part a) using Lagrange polynomials of order 1-3, but ONLY solve by hand