Some basic information is that the game starts with 6 inventory slots and the first additional slot (7th slot) costs 400 coins, the 8th slot costs 857, the 9th 1339, and so on.
The game is called Sol's RNG (Link Here).
I am trying to figure out if there is an equation that would fit this kind of pattern. I think it's exponential but I am unsure.
I have graphed these out onto Desmos up to the 42nd term (Link Here), but I am unsure how to proceed with the calculations. Hoping someone can help!
Cheers!
The formula
$$ y=\left\lfloor 400(x-6)^{1.1} \right\rfloor $$
fits the data exactly. Here's Desmos link. You can do the fitting in Desmos. It came close enough to allow to guess the "correct" values (when you also put the floor in there).