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Message: <blockquote data-quote="orsal" data-source="post: 2323901" data-attributes="member: 16016">It's clearly not exponential. It increases faster than a linear relationship, but not that much faster. Look at the ratios of consecutive terms. At the beginning of your chart, the ratios are: infinite, 3, 2, 1.67, 1.44, and so on, gradually getting smaller. At the end, the ratios are around 1.05. In an exponential progression, that ratio is constant. It's even more clearly not logarithmic. It does increase faster than a linear progression (in other words, the difference between successive terms increases), whereas logarithmic growth slows down. I'd think some sort of power function, y=b*x^n where b and n are constants. (Cheiromancer's suggestion is an example) They all grow. The higher n is, the faster they grow, so n>1 gives you something higher than linear (n=1 is linear). However, they are nowhere near exponential in their rate of growth. The ratio between successive terms in a power sequence eventually gets close to 1, which is what is happening here, although the difference between successive terms gets bigger and bigger. My first guess would be to try a quadratic expression, because the first few terms exactly fit a quadratic pattern (the differences form a linear relationship). But for level 6 we get 13,000, instead of 13,500, and then start increasing rather faster. Extrapolating the formula 450*x*(x-1), which perfectly fits the first 6 terms, would give us only 171,000 at level 20 (less than 1/4 the official value) and 2,844,000 at level (less than 1/80 the correct value). But with regression on the logarithms (note: any time y is a power function of x, log<img src="https://cdn.jsdelivr.net/joypixels/assets/8.0/png/unicode/64/1f44d.png" class="smilie smilie--emoji" loading="lazy" width="64" height="64" alt="(y)" title="Thumbs up    (y)"  data-smilie="22"data-shortname="(y)" /> is a linear function of log(x)), I get that the best fitting power function is y=14.318*x^3.74. (Here y=wealth, x=level.) The correlation is 0.994228, indicating a very good fit (an exact linear relationship would have correlation 1). Maybe you'd prefer an integer exponent. In that case, the best formula of the form y=b*x^3 is with b=185.6658; the best formula of the form y=b*x^4 is with b=5.8109. Of course, you could round these numbers off as you see fit.</blockquote>

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