@kflo you know how yesterday I was trying to generalize the notion of "decaying as it would have otherwise at the same quantity had it not accumulated in the first place". In my judgement that approach could easily fall apart in certain circumstances; if you attach a pure exponential (a prototypical example) to a higher point it probably won't go to zero in the long run as it should because the asymptotic behavior will merely be shifted up.
I
think I have come up with a general procedure.
Instead of "decaying as it would have otherwise at the same quantity had it not accumulated in the first place" I propose that it would "decay is it would have otherwise at the same quantity had we stopped accumulating at the previous dose......this is done iteratively". There's some in between steps to make sure everything is "lined up" but that's the long and short of it.
The idea is not solidified/tested. All I know is that it will be a bitch to program.
Here's some shitty pictures to illustrate. I hope the behavior of the actual program lines up with what I think should intuitively happen in two typical cases.
First the trivial familiar one.
Now the actual one I'm trying to deal with.
I really hope this idea works. At least with this idea there is a vague feeling of consistency/symmetry between how something accumulates from multiple doses and how it decays; It accumulates iteratively from previous doses and it decays iteratively from previous decays.
Hopefully my intuition works.
