[epgui]

That first sentence could replace the entire paper. Growth functions are inherently/fundamentally exponential (regardless of whether we're talking about bacterial colonies, populations of rabbits, compound interest or ROI), but the forces that act on the exponent change over time. It really is this simple.

[marginalia_nu]

Real exponential growth is fairly rare outside mathematical models, it is almost always attenuated by logistical bottlenecks or resource scarcity after some initial phase.

[lupire]

That applies to linear growths too. In the long run almost everything is eventually a constant, approximately step function from intitial to terminal condition.

[epgui]

Sure, but I'd then make the same (modified) argument.

[ravi-delia]

That's not really true though. Regardless of whether our growth is exponential or logistic, we haven't hit an inflection point yet. So if the past data is better fit by a linear function, the logistic nature of our growth can't be the reason.

[jacobolus]

> Growth functions are inherently/fundamentally exponential but the forces that act on the exponent change over time

By this standard, every function is “fundamentally exponential”.

You can plot literally any (strictly positive, differentiable) function on a log scale and find the slope at every point. BAM! Look, an exponent (changing over time)!

[epgui]

Don't be facetious. In real life, the forces acting on the exponent correspond to real things that are related to the thing we're observing grow.

If you don't have a causal graph explaining why your exponent is changing, then your plot doesn't make sense.

[jasonwatkinspdx]

Oh, and what proof do you have to offer that those exponentials are not sigmoids?