# Thread: Hi I'm new and have a problem with exponential equation.

1. ## Hi I'm new and have a problem with exponential equation.

So I'm a Swede and found this site in an attempt to solve a game problem.

I have a weapon that do 50 dps and damage more per second to a maximum of 200 dps and it maxes out in 45 seconds.

200 - 50 = 150
150 / 45 = 3,33...

So it does 3,33 extra damage per second. Now i want to know how much damage it does after let say 10/s.

50 * 10 + (3,33*10) = 533,33

This sounds wrong since every tick in seconds make it damage more the damage should be closer to.

50 + 3,33
100 + 6,66
150 + 13,33
200 + 26,66
250 + 43,33
300 + 96,66
350 + 183,33
400 + 376,66
450 + 723,33
500 + 1446,66

This way I believe I might get a more accurate number but this is tedious and prone to error since it's done manually and you probably will count something double.

How do i make this calculation with equation?

Side note: If I want to damage lets say 750 and want to know the time until it's reached how do I change the equation to reflect the new wanted output?

2. ## Re: Hi I'm new and have a problem with exponential equation.

I don't know if I understood your problem, but from what I did understand. It looks like an arithmetic progression to me.https://en.wikipedia.org/wiki/Arithmetic_progression

Let $d_t$ be the damage your weapon does in the second t. We know that $d_1=53.33$ and we also know ( from what I understood ) that $d_n=d_{n-1}+3,(33)$. Using this formula $d_{45}=200$ ( I think that $d_n=200$ if n is bigger than 45 ), which seems right. To find how much damage it does after 10s you just need to compute $d_{10}$, which is pretty easy since $d_{10}=53,(33)+9*3,(33)$.

Since your weapon reach a maximum of 200 dps, I assume that you want to know how much seconds will it take to deal a total damge of 750. To find out you need to solve this inequation for k.
$\sum_{t=1}^{k}d_t \geq 750$