Problem $1$: The following data was determined experimentally and represent discrete values of a function for which no formula is known:

$($THE DATA TABLE IS IN THE PICTURE PROVIDED$)$

You can use linear interpolation to approximate the value of the function f$($x$)$ for any value of x that falls between the smallest and largest value available in the table. The procedure is as follows:

$1.$ Find the two x$\text{'}$s in the table between which the given x value falls. These are called xi and Xi$+1.$

$2.$ Identify the corresponding values of f$($x$,)$ and f$($xi$+1).$

$3.$ Perform interpolation between these to find the value of the function using the following formula:

$($THE FORMULA IS ALSO IN THE PROVIDED PICTURE$)$

Develop the program that calculates the approximation of the function for the following values of x$\text{'}$s:$-7\mathrm{.}8,13\mathrm{.}65,23\mathrm{.}5914,25\mathrm{.}085,$ and $33\mathrm{.}8.$The program will be executed for each of these values, that is$,$ five times.If the value of x is outside the range of values in the table, the program should output a message. The IDE console can be used to get the outputs where the value of x and the corresponding result should appear.Solve the problem using two one$-$dimensional arrays, one that holds the x$\text{'}$s and another that holds the f$($x$,)\text{'}$s$.$ The values must be read from an external file.