Isn't there a stationary and decline phase missing on that chart ?. I guess it will hold true if we can get out of the petri dish.
Then again, who is to say that biological life is the end result, maybe we are just a stepping stone and it will be digital life that conquers the stars, leaving us and earth behind like a discarded cocoon
Depends upon what you are looking at. This is an exponential curve which is most often a part of a larger S curve. So with individual technologies, as an example, we see what you describe: a growth phase following by a slowing and eventual decline. This is why S curves overlap.
But the next result, when stepping back, is an exponential.