If you do a ExpReg you get y = 14837.73(0.80851^x) which has SSE = 6431130.
Using a couple data points, (1,11500) and (16,600), that appeared to be a good visual fit to estimate a,b I got y = 14002.35(0.82129^x) which has SSE = 6302004.
The point is that the visual fit gave a smaller SSE than the regression on the transformed data. There is nothing special about this data. You can do this with any data set that "appears" to be exponential but has some deviation from the exponential model.