[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.