How can I calculate the cost of a business upgrade in Adventure Capitalist?

Solution 1:

It's the upgrades

You might have forgotten to count in the effect of the two angel upgrades:

• Laser Swap (gives +10 giant lasers for 50 * 10^15 angels)
• Laser Exchange (another +10 giant lasers for 25 * 10^24 angels).

Upgrades that grant additional business facilities do not increase the price of buying additional facilities to make it so that it does not matter when you get these upgrades. This exactly accounts for your discrepancy. You should calculate as if you have 380 lasers (there are 20 'free' extra ones in there from the angel upgrades).

10^12 * 1.5^380 = 8.21634e78 (cost of #401)
10^12 * (1-1.5)^390 / -0.5 - 10^12 * (1-1.5)^380 / -0.5 = 9.31159e80 (cost of 401-410)
10^12 * (1-1.5)^480 / -0.5 - 10^12 * (1-1.5)^380 / -0.5 = 6.68089e96 (cost of 401-500)

These seem to match the game's numbers (Nissa's answer tipped me off here).

Sidenote about why angel upgrades giving businesses work this way:

If this weren't the case then you would have to skip the upgrades and buy them last to get the most benefit out of them (after all, your 400^th laser is quite a bit more expensive than your 1^st), making getting your upgrades a tedious process. Now you can just click 'buy all' with every reset once you unlock the button and don't worry about it.

Solution 2:

[E]ither the coefficients are just approximations, I am calculating something incorrectly or possibly both.

The latter for sure.

All of your calculated amounts with a coefficient of 1.5 are off by a factor of 3,326±3. This makes me wonder if you put in the right parameters.

However, even more convincing is that this number is within 0.1% of 1.5²⁰—the ratio that you would see from 20 additional Giant Lasers.

So: triple-check your spreadsheet, and if you can’t find anything wrong, post it here for further examination.