Problem $4$:

For the following data

$\backslash$table$[[$x$,0\mathrm{.}1,0\mathrm{.}2,0\mathrm{.}3],[y=e^x,1\mathrm{.}1052,1\mathrm{.}2214,1\mathrm{.}3498]]$

A$.$ Write a program to determine natural cubic spline interpolation function.

B$.$ Write a program to determine quadratic spline interpolation function.

C$.$ Find $f(0\mathrm{.}15)$ in each case and state which case is the best fit?