$($By Matlab$)$ Polynomial vs$.$ piecewise polynomial interpolation; FNC $5\mathrm{.}1\mathrm{.}2)$ The following table

gives the life expectancy in the U$.$S$.$ by year of birth

$($a$)$ Defining "year since $1980"$ as the independent variable, use polyfit to construct and plot the

polynomial interpolant of the data.

$($b$)$ Use interp$1$ to construct and plot a piecewise cubic interpolant $($use 'spline' option$)$ of the

data.

$($c$)$ Use both methods to estimate the life expectancy for a person born in $2007.$ Which value is

more believable?