So I have a table of data that I'm 99% sure is formulaic:

1 51
2 129
3 235
4 368
5 547
6 768
7 1038
8 1414
9 1811
10 2352
11 3041
12 3863
13 4892
14 6108
15 7611
16 9540
17 11808
18 14673
19 18143
20 22329
21 27356
22 33703
23 41278
24 50493

If you graph this, it makes a VERY nice curve. I used excel to put a trendline on it, but none of the options there match up perfectly. A 6th order polynomial is close, but not quite. Anyone here able to get a better equation on this data? I tried taking a log of it and that's CLOSE to linear, but not quite.

if you're wondering, this is from a browser game called Ikariam. These are the prices in wood for a certain building at different levels. I suspect that they have an equation they use to determine it and that once I get an equation for one building, the rest will be similar. I'm trying to extrapolate to get the cost for higher levels than they publish the values for...

Just in case anyone else needs the data in a better format...

So I did some research on Excel commands, and there is a GROWTH command that might work. I tried it and don't like the first result for stage 25, but you might start there. Not sure I have more time to work on it.

Some googling of "line of best fit" that might help too.

A program like Mathematica might help. Mathematica costs money, but Maxima doesn't and can do most if not all of the same:

http://maxima-project.org/wiki/index.php?title=Maxima_FAQ

I'd help more if I could.

Keep in mind the equation may change for higher levels, so equation 1 for the first X levels, then equation 2 for the next X levels...

that's possible, but the curve the data makes sure looks smooth to me. Some sort of exponential probably...

if you throw the data into Excel and plot it - then add a trend line as shown here

http://allyourtech.com/content/articles/21...spreadsheet.php
you can get a very good estimate of the line based on the given data

y = 0.0005x^6 - 0.0205x^5 + 0.4955x^4 - 4.5186x^3 + 36.346x^2 - 17.792x + 41.651 (R2 = 1)

Good Luck