This is a plot of 2^x with the y-axis scale changing. The red X is a point at approximately 2^39 that is on the line.
Notice that the curve looks identical at many different scales, except for a translation on the x-axis. Any place where one might point to the "knee" of the curve is on the "flat line" portion or the "huge slope" portion at different scales.
FreeMat/MATLAB code so you can generate this plot yourself.