I am bothered the animation does not include confidence intervals or error bars for the fit. The way these confidence intervals would shrink as more data points are available would tell a just as important part of the story.
yes, a better problem definition would in this case reveal that the estimate becomes quite good (in my definition) around the 50% time mark, when the transition from ^x to ^-x takes place. More specifically, I mean that although the stable point is still off by e.g. 25%, the important thing is that the stable time of the curve is well-estimated. you know it's no longer increasing exponentially...
