Comment by boerseth

> Hyperbolic growth is what happens when the thing that's growing accelerates its own growth.

No. That is quite literally exponential growth, basically by definition. If x(t) is a growing value, then x'(t) is it's growth, and x''(t) its acceleration. If x influences x'' , say by a linear relation

x''(t) = x(t)

You get exponentials out as the solutions. Not hyperbolic.

I always thought of the exponential as the pole of the function "amount of work that can be done per unit time per human being", where the pole comes about from the fact that humans cease to be the limiting factor, so an infinity pops out.

There is no infinity in practice, of course, because even though humans should be made independent of the quantity of extractable work, you'll run into other boundaries instead, like hardware or resources like energy.