An NYT article about a text-message-based ad that aired during the Super Bowl talks about the high follow-through rate that the ad earned for its creator, the NFL. In fact, the ad did so well that one executive described it like this:
While Mr. Berman [general manager of NFL Digital Media] declined to say exactly how many people went ahead and signed up, he said the number was “exponentially higher” than the 2 percent conversion rate for most Web sites.
What does "exponentially higher" really mean in the context of a single number? Is 4 "exponentially higher" than 2? Is 6? Is 10? Maybe. The trouble is that they are all "linearly higher" as well (yes, I'm making terms up). The problem here is that to describe a pattern or growth as exponential requires a few datapoints. In fact, it even takes multiple observations to characterize something as linear! The most we can say about a single observation is that it is some multiple of another, baseline measure. To say a single number is "exponentially higher" than some other single number doesn't actually have any meaning at all!