There's a problem with using exponential growth, which can be illustrated like so
Imagine the blue line is Level, becoming less profitable over time. Eventually of course it won't be worth doing at all, often happening surprisingly suddenly and soon. As an extreme exaggeration: If a player can earn 100xp/second by killing stuff with their continuous beam atomic ray gun, how long will it be before the player's character no longer levels up in a 40-hour week of gaming? Briefly, with a doubling xp/level rule, that's 14million xp/wk, taking the character to level 23. It will be several weeks before level 25, and over a hundred years of 8-hour days to get to level 30.
What happens along the way is that prize xp is increased (the red line in the graph) in an attempt to create the more linear balance (the gold line) for player level progression. But as time goes by, the difference between red and blue becomes very large in different directions, and it becomes apparent that x^2 - log(x) is not a linear graph. Also, as the two competing forces diverge, even the most subtle random variances throw the thing out of balance. Eventually the whole formula engineering thing is tossed out the window, and the developers rely almost exclusively on quest and level-specific xp opportunities to arrive at the level-up time frames.
So rather than go through that whole rediculous bit of re-discovering that exponential diminishing returns models are problematic, just make a table of how long the player will wait to get their next reward, and assign level-ups to it.