The Math Behind Pokemon Levels

Calculus Level 4

When Pokemon was being designed, its creator Satoshi Tajiri had to make decisions about the gameplay. He decided that the amount of experience points which a defeated Pokemon yields should be directly proportional to its level. He also wanted the gameplay to last longer at higher levels, and decided that in order to level up, the number of Pokemon you needed to defeat should be directly proportional to your level.

Based on these decisions, he created EXP(L), which denoted the total number of experience points you needed to reach level L. What is the shape of EXP(L)?

Image credit: Indie Games Ichiban
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