Unity RPG-style Level System (Generic version)

using System;
using System.Collections;
using System.Collections.Generic;
using UnityEngine;

public class LevelSystem
{
    int lvl;
    int exp;
    int expn;
    int totalExp;
    const int MAX_LEVEL = 100;

    public LevelSystem()
    {
        SetStartingExperience();
        Debug.Log("Level: " + lvl + " Experience: " + exp + " Experience Needed: " + expn + " Total Exp: " + totalExp);
    }

    public void SetStartingExperience()
    {
        lvl = 1;
        exp = 0;
        expn = GetExperienceNeeded(lvl);
        totalExp = exp;
        return;
    }

    public void AddExperience(int amount)
    {
        exp += amount;
        totalExp += amount;
        ExperienceCheck();
    }

    private void ExperienceCheck()
    {
        if(exp >= expn)
        {
            LevelUp();
        }
        else
        {
            return;
        }
    }

    private void LevelUp()
    {
        if (lvl == MAX_LEVEL)
        {
            return;
        }
        if (lvl != MAX_LEVEL && exp >= expn)
        {
            lvl += 1;
            exp -= expn;
            expn = GetExperienceNeeded(lvl);
            Debug.Log("Player gained a level! Player is now Level " + playerTamer.lvl);
            ExperienceCheck();
        }
    }

    private int GetExperienceNeeded(int level)
    {
        double baseXP = 500.0;
        double exponent = 2.0;
        level++;
        int newExp = (int)Math.Ceiling(baseXP * (Math.Pow((double)level, exponent)) - (baseXP * (double)level));
        return newExp;
    }
}