Rationale for the exponential annealing function from lesson 9?

Hi there,
I’m a bit confused about the sched_exp function found in notebook “05_anneal”, its rationale and application.
Unlike the other anneal functions, it produces different curves for different start and end values (see this graph I was exploring it with) and it is not defined at start=0, since there is a divide by start value in the function:


Is there a reason for this? Has exponential annealing been explored and applied much? The function doesn’t get used again in the notebooks, from what I can see.
Why not scale between start and end values with a continuous function which has an exponential curve, which is defined for 0 ≤ x ≤ 1, and which satisfies f(0) = 0, f(1) = 1, similar to the other annealing functions?