AMC 12 2008b Problem 24

Let $A_0 = (0,0)$. Distinct points $A_1,A_2,\ldots$ lie on the $x$-axis, and distinct points $B_1,B_2,\ldots$ lie on the graph of $y = \sqrt {x}$. For every positive integer $n$, $A_{n - 1}B_nA_n$ is an equilateral triangle. What is the least $n$ for which the length $A_0A_n\ge100$?

(Solution)

\textbf{(A)}\ 13 \textbf{(B)}\ 15 \textbf{(C)}\ 17 \textbf{(D)}\ 19 \textbf{(E)}\ 21