Making a level progression system similar to Bravely Default’s

So I am working on an RPG and I want the level up system to be similar to Bravely Default’s, which must be similar to how FF classically levels up characters.

What I know about the level up in the game is that.

  1. The game starts of with a large exp pool to fulfill, and the enemies give large drops of exp too (ex: in lvl 1 areas enemies give 50-150 exp points, and you need around 500 exp to reach lvl 2 and so on)
  2. The larger the level, the more exp you will need (to the point you need x0 000 exp points to continue in the midgame), however in the late game, the exp point does not increase exponentially (let’s say it doesn’t reach x00 000 not even at level 99)

Obviously, we want more effort to gain more levels, but this is more about assigning the enemies appropriate exp points depending on the region of the game.

Currently my algorith is lvl = constant * sqrt(exp), however I feel this formula doesn’t work for very large numbers.