Suppose we walk to reach next milestone. Each next milestone is increasinlyincreasingly farther away (function slows down). Specific example: You need 1$1$ step to reach first point, another 2 steps to reach second point, another 3$3$ steps to reach third point, etc. If iI know the amount of steps iI have passed, how can iI know which milestone i'veI've passed? This is the function that solves the problem but all day long iI cannot find what this formula is:
It looks so incredibly simple! and yet iI couldn't derive nor find anything about it!
But the question is more general than this. What if iI want less contrast and the slowing down of Y not to be 1X$1X$, but maybe 0.5X$0.5X$?
iI know my terminology might be wrong, but this is precisely why i'mI'm asking this question, because iI don't even know what those functions are called, what that growth is called, and how to google it at all. I've found nothing. Maybe there's some formal terminology that iI don't know of, and if it's not some 1 to 1 duplicate question in face of more well-stated question, then iI expect a highly detailed answer on this: How to approach such problems, how to find such formulas, and how to fine-tune them to get any consistent slowing-down growth functions.
