The amount of federal tax per capita $($per person$)$ can be modeled by the function $S=7\mathrm{.}8247t^3-54\mathrm{.}78t^2+525\mathrm{.}76t+5166\mathrm{.}8$ where $t$ is the number of years after $1995.$

a$.$ What are the values of $t$ that correspond to $2007,2013,$ and $2020?$

b$.S=f(7)$ gives the value of $S$ for what year? What is $f(7)?$

c$.$ What $x_{\text{m}\text{i}\text{n}}$ and $x_{\text{m}\text{a}\text{x}}$ should be used to set a viewing window so that $t$ represents $1995-2020?$

a$.$ What value of $t$ corresponds to the year $2007?$

$t=$