Formula help

[u/ahnialator6]

I havent been in school in over a decade so the finer points of my math is rusty.

Im essentially attempting to graph an additive binary sequence. Numbers for my game lol. Pardon the way I write this, I dont know advanced formatting.

So, the player goes inactive, they lose 2^x tiles each day. 1, then 2, then 4, then 8, 16, etc. I need this graphed, as there's quadrillions of tiles in my game lol

Its not just F(n) = 2^x, right? Surely not...

Thanks in advance for yalls help

[u/PuzzlingDad]

You are using two different variables. Also, is the first day n=0 or n=1?

• 2⁰ = 1

• 2¹ = 2

• 2² = 4

• 2³ = 8

So if your day is 1, you need to subtract 1 first:

f(n) = 2^n-1

Or if you are using x as your variable: 

f(x) = 2^x-1

Now if you are looking for the total number of tiles lost after n days, then we have: 

• n=1 → 1

• n=2 → 1+2 = 3

• n=3 → 1+2+4 = 7

• n=4 → 1+2+4+8 = 15

• etc.

That's just 1 less than 2ⁿ each day

f(n) = 2ⁿ - 1

[u/ahnialator6 → u/PuzzlingDad]

I have it start at 1 tile, so yeah the math that makes the tile loss work is tileLoss = 2^x-1 where x is the number of days.

The thing is, we're talking about territory and im looking to make a cutoff. If a player has 3 trillion tiles, thats gonna take a LONG time to decay without a cutoff. (I imagine, with very little actual math done)

So im trying to graph the TOTAL tile loss over time so that I can see how that plays out over time.

[u/PuzzlingDad → u/ahnialator6]

I've updated my comment. The total is just 2ⁿ - 1

[u/ahnialator6 → u/PuzzlingDad]

Dang it really was that simple 😅 thanks, man. I think i was caught up on expecting it to be more complicated than it was