Answer
$\displaystyle \lim_{x\rightarrow+\infty}S(x)=573.$
Students living in households with extremely high income have an average SAT score that approaches $573.$
Work Step by Step
When $x\rightarrow+\infty,$
$e^{-0.013x }$ has the form $k^{Big\ negative }= Small$,
so $573-33e^{-0.013x }\rightarrow(573$ - small) $\rightarrow 573.$
$\displaystyle \lim_{x\rightarrow+\infty}S(x)=573.$
Students living in households with extremely high income have an average SAT score that approaches $573.$
