Fit the data below to a power function of the form $y=a{x}^b.$

$\backslash$table$[[x,30,50,93\mathrm{.}33,148\mathrm{.}89,315\mathrm{.}56],[y,1\mathrm{.}35,0\mathrm{.}28,0\mathrm{.}05,0\mathrm{.}012,0\mathrm{.}00075]]$

Determine the $R^2$ value for the model developed in question $2.$

For the data in the table below,

a$)$ Use $2^{nd}$ Order Lagrange interpolating polynomial to find $y$ at $x=65.$

b$)$ Use inverse interpolation by solving a quadratic equation to find $x$ at $y=27.$

$\backslash$table$[[x,40,55,70],[y,28,30,24]]$