$(2)(5$ points$)$ During the years from $2005$ to $2011($just before, during, and immediately after the recession years of $2007$ to $2009),$ the number of single$-$family houses sold decreased at a rate that can be modeled well by an exponential function. The number of single$-$family houses sold $($in thousands$)$ can be approximated by the function

$g(x)=1483e^{-0\mathrm{.}28x}$

where $x=0$ corresponds to the year $2005.$ What was the first full year in which the number of houses sold fell below $500$ thousand?

Give your answer as the year. Show all the appropriate algebraic work needed to solve the problem...NO guess and check...NO short cuts.