What's The Secret Behind Leveling Up Your Erratic Pokemon?

Algebra Level 3

Pokemon is a video game owned by Nintendo, in which you train a “Pocket Monster” who levels up when it has gained enough experience points from defeating the enemies. The amount of experience \(EXP_{Erratic}(L)\) that an Erratic Pokemon needs to reach L is given in the table below.

\( \begin{array} {| l | l || l | l |} \hline \text{Level} & \text{EXP} & Level & EXP \\ \hline 1 & 2 & 11 & 2369\\ 2 & 16 & 12 & 3041\\ 3 & 52 & 13 & 3823\\ 4 & 123 & 14 & 4720\\ 5 & 238 & 15 & 5738\\ 6 & 406 & 16 & 6881\\ 7 & 638 & 17 & 8156\\ 8 & 942 & 18 & 9564 \\ 9 & 1327 & 19 & 11112\\ 10 & 1800 & 20 & 12800\\ \hline \end{array} \)

Which of the following functions is the best approximation of \( EXP_{Erratic} (L)\) in the range \( 1 \leq L \leq 20 \)?

Image credit: Bulbagarden

Details and assumptions

If you are interested in Pokemon levels, you might want to look at: The math behind Pokemon levels

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