2008 AMC 12B 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?

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

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