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I figured out the formula for the cost of the next N of a business...
cost of N ≈ cost1 * (sum of 2^(n/5) from n=0 to n=N-1)
The works for the main game at least (haven't tried events).
Seems that the 5 in the formula isn't always exactly 5, and small changes to 5 greatly affect cost especially for large N.
For example, if the cost of 1 is 10, the cost of 25 will be about 2085...
https://www.wolframalpha.com/input/?i=10+*+%28sum+of+2%5E%28n%2F5%29+from+n%3D0+to+n%3D25-1%29
Anyway, on city 80, I used this formula to reason that I will get the "earn 50 AE" quest a bit before the "rank up 70 businesses" quest. 50 AE will take me over a month!
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