Math fun fact time:

Neither x^2 and x^200 are exponential growth, they are polynomial growth. 2^x or 200^x would be exponential growth. After a certain point, all exponential curves will outpace any polynomial curve.

So after a certain x, 2^x will outpace even x^200. This happens at around x=2224, after which 2^x will always be bigger than x^200.

If you know the rules for indices and logarithms, you can see why this is. We can take the logarithm of both functions which converts them both into slower forms that we can understand easily.

log(2^x) simplifies to x log(2), which grows linearly. However, log(x^200) simplifies to 200 log(x), which grows according to log(x), a painfully slow growing function that quickly grinds to a near halt.