[cbolton]

I would say the exponent of a variable makes (contributes to making) the result large.

[Haunted_Cabbage]

Given that a negative exponent makes a result smaller, I'd say that it describes rate at which it'll change.

[sethammons]

What if the base is less than one?

[cbolton]

I think the question "does it make it larger or does it describe how it gets large?" implies that the transformation is increasing.

[Haunted_Cabbage]

My intention was to say that the exponent describes the characteristics of a change, not to imply that the effects are only positive.