trouble is, you look at the growth curve for homo sapiens, it's a nice exponential not much different from the shape of the growth curve for yeast ---- so far. it's population vs time. worldwide, that is; not Italy, or Israel, or whatever, but no. of humans vs time since the beginning of time.
for the yeast, it's over in a day or so, under the right conditions.
for us, it's .... well, who knows? we'll see.
www.frogojt.com/yeast1.pdf
nice contolled growth curve for yeast, making hay while the sun shone.
i don't have a growth curve for the humans. I've seen it, from UN data and whatnot. Maybe it was in a biology book. The doubling time is now what, a hundred years, or fifty years? Must be levelling off; maybe not. Haven't looked for quite a while.
the growth curve for microorganisms usually gets pretty asymptotic, but that's because the bugs are running out of oxygen, i.e. shakeflasks. it's the kind of thing that becomes more and more limiting but not deadly.