I would imagine that population growth follows something like a sigmoid growth curve. Having birth rates slow down is to be expected once humans reaches carryin

I would imagine that population growth follows something like a sigmoid growth curve. Having birth rates slow down is to be expected once humans reaches carrying capacity. I wouldn't worry about humanity fading out - I mean, reaching a stable plateau would be great! The worry is that we'll overshoot that by too big a margin and suffer a big collapse.