> that has similar properties. You should be specific about what properties you're talking about. What you're saying is that any function increasing function

> that has similar properties. You should be specific about what properties you're talking about. What you're saying is that any function increasing function grows faster than some exponential function on a finite interval. Still, you can observe f(x) on x ∈ [0, 1] and see that it is growing linearly. And you can observe g(x) on ∈ [0, 1] and see that it is growing exponentially. I do not see the value in discussing the rate of exponential growth of f. Where as for g, there is a parameter with value ln(2). If data looks like f, don't try to fit an exponential function to it (whether it's a least-squares fit, or any other objective f > g. Are you trying to say anything else?