2015 Fermat Problem 13

At the end of the year 2000, Steve had \$100 and Wayne had \$10\,000. At the end of each following year, Steve had twice as much money as he did at the end of the previous year and Wayne had half as much money as he did at the end of the previous year. At the end of which year did Steve have more money than Wayne for the first time?

\textbf{(A)}\ 2002\quad \textbf{(B)}\ 2003\quad \textbf{(C)}\ 2004\quad \textbf{(D)}\ 2005\quad \textbf{(E)}\ 2006

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Full credit to this problem is given to the CEMC, you may view all Fermat contests here.