this post was submitted on 21 Mar 2024
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Mafs (sh.itjust.works)
submitted 9 months ago by [email protected] to c/[email protected]
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[–] [email protected] 19 points 9 months ago* (last edited 9 months ago) (2 children)

Good point and well spotted!

PS: Though it's not actually called exponential (as it isn't e^nr-3-month-periods^ but rather 2^nr-3-month-periods^ ) but has a different name which I can't recall anymore.

PPS: Found it - it's a "geometric progression".

[–] [email protected] 15 points 9 months ago* (last edited 9 months ago) (1 children)

By tweaking a few parameters you can turn every base into any other base for exponentials. Just use e^(ln(b)*x)

PS: The formula here would be e^(ln(2)/3*X) and x is the number of months. So the behavior it's exponential in nature.

[–] [email protected] -1 points 9 months ago* (last edited 9 months ago) (1 children)

By that definition you can turn any linear function a * x + b, "exponential" by making it e^ln(a*x +b) even though it's actually linear (you can do it to anything, including sin() or even ln() itself, which would make per that definition the inverse of exponential "exponential").

Essentially you're just doing f(f^-1^(g(x))) and then saying "f(m) is e^m^ so if I make m = ln(g(x)) then g(x) is exponential"

Also the correct formula in your example would be e^(ln(2)*X/3) since the original formula if X denotes months is 2^X/3^

[–] [email protected] 1 points 9 months ago (1 children)

It doesn't matter if you divide ln(2) or x by three, it's the same thing.

[–] [email protected] 1 points 9 months ago

Get a room you two

[–] [email protected] 3 points 9 months ago (1 children)

PPS: Found it - it’s a “geometric progression”.

A terminology that I learned from the Terminator 2 movie. Only that was, I think, a "geometric rate".

[–] [email protected] 2 points 9 months ago* (last edited 9 months ago) (1 children)

Chessboard and wheat

[–] [email protected] 2 points 9 months ago* (last edited 9 months ago)

One of the best mathematical stories from ancient times, IMHO,