In a game that I play, there is a power value that is an overall evaluation on how powerful your account is. There is a function where you can level up a skill, and levelling it up gives a bonus to your power rating. With help, I found exactly how much power is granted based on the level of the skill. I would like some help finding an equation or something to help me predict power levels at higher levels, and am having a hard time finding a correlation, but when I graphed it, the closest fitting line I got was a natural exponential.(I put them into ordered pairs for the sake of plotting points.) I put it into wolfram Alpha and it spat this plaintext out, so I'll just leave it here.
(1 | 100
2 | 130
3 | 180
4 | 250
5 | 330
6 | 500
7 | 700
8 | 930
9 | 1200
10 | 1500
11 | 1900
12 | 2370
13 | 2900
14 | 3500
15 | 4170
16 | 5000
17 | 6000
18 | 7170
19 | 8500
20 | 10170)
Maybe I have overlooked something, but I am not sure if there is a formula that fits, and I don't have nearly enough experience/knowledge to figure that out on my own.
You can find a best fit curve using a tool like Desmos. Trying a cubic polynomial gives you a nice fit (https://www.desmos.com/calculator/9yiibhrf6i):
with the equation
Calculators like Desmos use a method called least squares fitting, but you don't really need to know how it works to use it. You basically just need to know what type of equation (exponential, linear, etc.) you think best fits your data. For example, if instead of a cubic you tried an exponential of the form $y=ax^b+c$ your data is fit best by