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Feb 23, 2015 at 0:12 comment added Eckhard The numerics are also consistent with $x_n$ being bounded, so I'll defer to Robert Israel.
Feb 22, 2015 at 23:43 comment added Joseph O'Rourke @Eckhard: Good! Then clearly we need calculations to settle the issue for $e^{-x}$. It seems clear to me that some function will prevent the rays from bouncing to $x=\infty$, even if $e^{-x}$ does not.... Oh, I see Robert Israel has weighed in with calculations.
Feb 22, 2015 at 23:25 comment added Eckhard Just as empirically, I believe that numerical calculations are consistent with a logarithmic divergence of the $n$th reflection abscissa.
Feb 22, 2015 at 22:43 history edited Joseph O'Rourke CC BY-SA 3.0
Added "quickly" because if slowly, then maybe would diverge.
Feb 22, 2015 at 21:38 comment added user64494 @ Joseph O'Rourke: Thank you for your interest to the question.
Feb 22, 2015 at 21:22 history edited Joseph O'Rourke CC BY-SA 3.0
added 9 characters in body
Feb 22, 2015 at 21:17 history answered Joseph O'Rourke CC BY-SA 3.0