2008 AMC 8 Problem 12

A ball is dropped from a height of 3 meters. On its first bounce it rises to a height of 2 meters. It keeps falling and bouncing to \frac{2}{3} of the height it reached in the previous bounce. On which bounce will it rise to a height less than 0.5 meters?

\textbf{(A)}\ 3 \qquad \textbf{(B)}\ 4 \qquad \textbf{(C)}\ 5 \qquad \textbf{(D)}\ 6 \qquad \textbf{(E)}\ 7

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.