please make sure that the answer is true and show every step .thank you.

Use the following set of pressure-volume data to develop a script m-file to find a₀ and a₁ in the following exponential model.

After the model development;

Calculate the root of developed model equation using Newton-Raphson method (x_initial=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 (bar)	Volume (m3)
0.644	32
0.985	25
1.108	22.2
1.363	18
1.631	15
1.934	12
2.356	9
3.1	7.2

Note: The script m-file should work itself and all inputs must be defined in the beginning of the code.

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):

a- the model, with a₀ and a₁ 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.

these should be answered:

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: