NUMERICAL ANALYSIS TUTORIAL EXAM Use the following set of pressure-volume data to develop a script m-file (name it as your "name surname") to find an and a in the following exponential model. y = a, + ax + axa After the model development; Calculate the root of developed model equation using Newton-Raphson method (Siritia=0). Then, the code should automatically calculate the predicted volume @ 1.05 bar pressure using the regression model. Also, in the same script m-file this value must be calculated using Lagrange Interpolation and the absolute difference between two finding must be displayed as well. Data Pressure Volume (bar) (m) 0.644 32 0.985 25 1.108 22.2 1.363 18 1.631 1.934 12 2.356 9 3.1 15 7.2 Note: The script m-file should work itself when I run it! I will not make any additional inputs. All inputs must be defined in the beginning of the code. Please note the following warnings! The results should be presented with fprintf command. The following results should be displayed at the end of the code in this order (just these. No more!): a- the model, with ag and ai written on it b- root of the model equation C- result of the predicted volume at 1.05bar using regression model d- interpolation result of volume at 1.05bar using lagrange method, e- the absolute difference between the volume values calculated from model and interpolation. ANSWER When script executed above text with correct result should be displayed on command window: a) The Model: y=(.........) + (...........) *x+ (..........) *x^2 b) root value : c) From model: V=....... when P=1.05bar d) According to LAGRANGE Method f interpolated value for p = 1.05 -> V= e) absolute difference between calculated value and interpolation difference