Neatly showing why when all you have is two data points you can’t just assume the best fit function for extrapolation is a linear one.
Mind you, a surprisingly large number of political comments is anchored in exactly that logic.
Doubling every three months is an exponential interpolation and not a linear one!
Good point and well spotted!
PS: Though it’s not actually called exponential (as it isn’t enr-3-month-periods but rather 2nr-3-month-periods ) but has a different name which I can’t recall anymore.
PPS: Found it - it’s a “geometric progression”.
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.
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 em 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 2X/3
It doesn’t matter if you divide ln(2) or x by three, it’s the same thing.
Get a room you two
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”.
Chessboard and wheat
One of the best mathematical stories from ancient times, IMHO,
Huge if true!
It looks like he aged 5 years in 3 months…
As a father I can confirm this seems right
Do we tell him?
That it’s not Christmas anymore?
Why is the wreath still there?
3 months of chronic sleep deprivation
How’re the kids?
His son’s face looks like that’s not the first time dad tell that joke.
“i’ve heard that before, dad.”
3 month milestone: baby is so over it
7.5 trillion pound coins is a lot, I wonder how much they weigh.
Math checks out.
TWICE!
Original post is not linearly interpolating but exponentially.
Bless the Maker and His water. Bless the coming and going of Him. May His passage cleanse the world. May He keep the world for His people.
Dude what? Where did this come from?
It’s a Dune quote for when the fremen see sandworms. The guy is saying his kid will weigh several tons, so logically he will evolve into a sandworm.
He dumb AF.
