$(10$ points$)$ Hugh Quackman opened a savings account on January $12003$ and made an opening deposit of $10,000.$ On June $302003,$ Quackman made a withdrawal of $2000,$ and on June $302004,$ Quackman made a withdrawal of $x.$ The fund grows according to the force of interest

$(t)=\{\begin{array}{cc}0\mathrm{.}05,& 0t<mn\; id="EditorElement\_14094725">1</mn>\\ \frac{0\mathrm{.}02t}{1+0\mathrm{.}01t^2},& t1\end{array}$

where $t$ is the time in years since January $12003.$ The amount of interest earned for the savings account between July $12004$ and December $312004$ was $81\mathrm{.}58353573.$ Find $x.$