How can you assert that a fit with one model is lesser fit than a fit with another model? Define 'lesser'?
The best fit is when you have a better R-squared value than any other fits. Excel calculates the best fits for every model automatically, so you can just conclude that a log-linear model has a better fit (0.94) than log-logistic (0.73).
If I am not mistaken, the best R-squared (least error from the data points) would be an N-degree polynomial for N data points such that the curve passes through every point.
Thus 'best fit' may have no correlation to predictive power.
Surely you of all people understand the concept of overfit...
Exponential growth is not some "arbitrary function." It is the solution to a very simple--and very meaningful--differential equation. It occurs whenever the growth rate of something is proportional to the size of the thing that's growing: e.g., the population of bunny rabbits in a park, bacteria in a petri dish, or users of a social networks.
My mathematical point to Risto is that the relatively lesser fit of 0.73 for the log-logistic exponential model is entirely meaningless because precisely the choice of model is what matters. So aminorex and Peter R have supported my argument.
P.S. kudos to Peter R's generative essence abstraction.