I was going to suggest that maybe it could be a known and published result in dynamical systems / population dynamics literature, but I am unable to find anything with Google, and textbooks I have at hand, while plenty mentions of logistic growth models, do not discuss prediction from partial data before inflection point.
On the other hand, it is fundamentally a variation on the themes of difficulty in model selection with partial data and dangers of extrapolation, which are common in many numerical textbooks.
If anyone wishes to flesh it out, I believe this behavior is not limited to trying to distinguish exponentials from logistic curves (or different logistics from each other), but also distinguishing different orders of growth from each other in general. With a judicious choice of data range and constants, it is not difficult to create a set of noisy points which could be either from a particular exponential or a particular quadratic curve. Quick example: https://raw.githubusercontent.com/aa-m-sa/exponential_weirdness/master/exp_vs_x2.png (And if you limit data point range you are looking at to 0 to 2, it is quite impossible to say if a linear model wouldn’t also be plausible.)
I was going to suggest that maybe it could be a known and published result in dynamical systems / population dynamics literature, but I am unable to find anything with Google, and textbooks I have at hand, while plenty mentions of logistic growth models, do not discuss prediction from partial data before inflection point.
On the other hand, it is fundamentally a variation on the themes of difficulty in model selection with partial data and dangers of extrapolation, which are common in many numerical textbooks.
If anyone wishes to flesh it out, I believe this behavior is not limited to trying to distinguish exponentials from logistic curves (or different logistics from each other), but also distinguishing different orders of growth from each other in general. With a judicious choice of data range and constants, it is not difficult to create a set of noisy points which could be either from a particular exponential or a particular quadratic curve. Quick example: https://raw.githubusercontent.com/aa-m-sa/exponential_weirdness/master/exp_vs_x2.png (And if you limit data point range you are looking at to 0 to 2, it is quite impossible to say if a linear model wouldn’t also be plausible.)