Problem $5$: Standard Interpolation Polynomials $[1$ pt$]$

In an experiment, we took the following five measurements to quantify the relation between the power

generated by a windmill and the wind speed:

Suppose that a fourth$-$order polynomial is proposed for interpolation:

$y=a_0+a_{1}x+a_2{x}^2+a_3{x}^3+a_1{x}^4$

Determine the coefficients, $(a_0,a_1,a_2,a_3,a_4),$ by hand. Hint: you may use MATLAB to assist you with some

of the matrix calculations, similar to Problem $4.$