How to say "become smaller/lower" in one word in mathematical context?

Question

We can say e.g. "You can see $2^x$ outgrowing $x^2$ as x increases in Fig. 6.18.".

How can we express the opposite?

The corresponding example: "You can see $x^2$ ... $2^x$ as x increases". What is a good single word for the gap?

Answer 1

"Outgrowing" is probably best interpreted as "the difference between $2^x$ and $x^2$ grows larger as $x$ increases". If you represent this difference as a formula $2^x-x^2=d$, then the converse, given by the formula $x^2-2^x=-d$ would be "the difference between $x^2$ and $2^x$ decreases as $x$ increases; i.e. $2^x-x^2>x^2-2^x$ for some $x$, and all $y>x$.

Answer 2

How about just "decreases"?

Maybe what you really want to say here is that the increases or decreases are exponential. The difference between, say, $2^3$ and $3^2$ is famously small, but the difference between $2^G$ and $G^2$, where $G$ is a googolplex, are mind-boggling, at least for puny human minds.