re: "how do you know anything of this?" https://en.wikipedia.org/wiki/Natural_logarithm http://ccnmtl.columbia.edu/projects/biology/lecture1/expogrow.html
There's a nice little graph all the way at the bottom of the second link.
I was thinking of a remark a professor made when I was studying electrical engineering in college many years (decades) ago. In this case the log function was being applied to capacitive decay but also applies to many natural processes, everything from oil well depletion to cell division and cell death in biological populations, (along with the Bell distribution curve).
Then there's the berry picking example. You go out to the patch every day. You always find berries but as each day goes by it takes longer and longer to fill your bucket.
I anticipate nay-sayers at some point are going to complain that improvement on some measures that apply numerical values are slowing down but if that's the case, it's actually normal and to be expected. imo
Simply put, in general, wouldn't you agree that the sicker you are, the longer it takes to get better. I'm thinking, the same with how long a neural cell has been sick, vomiting out amyloid plaque and eventually choking on it on top of its original malaise. Obviously, all the cells don't all fail at once. There's an onset, then a getting worse over time. There may even be some kind of prion/protein misfolding cascade going on that needs to be undone. A branching out process - run the film in reverse.