Uestion 2 120 marks underground cable breakdown often occur due to the unpredictable deterioration rate of the cable insulation. cable replacement can be very costly without regular mainte a 9-month study on an underground cable insulation had been conducted to check for the length of the cable insulation that have been deteriorated using fluorescence microscope in order to estimate the maintenance cycle. table 1 shows the data measured every 3 months during the study table 1 time, t (month) deteriorated cable insulation length, i 1.35 3.72 7.28 15.45 (a) generate a third order polynomial using newton's interpolation method to describe the variable of the deteriorated cable insulation length, (t) with respect to time (in month). write the polynomial in the form of at3btct d, where [10 marks] a, b, c and d are constants. (b) according to regulation, the cable insulation requires replacement if it is degraded by 6 mm. calculate the replacement time using newton raphson method with initial guess of 6 months from the polynomial generated in part (a). perform three iterations only and calculate true percent relative error for the final iteration answer [10 marks if the true value of the replacement time is 5 months.