Refer to the vandamore code below for reference and approach. The activity of the sun $($sunspots$,$ solar flares, and coronal mass ejection$)$ fluctuates in

cycles of around $10-11$ years. Sunspot activity can be modelled by the function ${?}^1$ :

$N(x)=57\mathrm{.}7sin[0\mathrm{.}602(x-1\mathrm{.}43)]+58\mathrm{.}8,$

where $x$ is the number of years since January $1,1997,$ and $N(x)$ is the number of sunspots

observed at time $x.$

The table below shows the value of $N(x)$ for $10$ distinct values of $x.$ Modify the Octave code

we developed $($in the relevant MAT$212$ Tutorial$)$ for the Vandermonde method to answer the

question that follows, please find the code below. Your code must make use of the format long command and $7$ decimal

place rounding.

$**$If $P_9(x)={\displaystyle \underset{i=0}{\overset{9}{}}}{a}_i{x}^i$ is the unique interpolating polynomial for $N(x)$ at the $x-$values shown

in the table, then what are the values of the coefficients $a_i,i=0,1,$dots,$9?$ Write them down

on your answer script. The relevant MAT$212$ tutorial code ifollows the question.