"Exponentially Better"

Dear residents in my little area of the country,

I keep hearing you use the word exponential in reference to a drastic change from one examined point in time to another.  For example, "I slept exponentially better last night than I did the night before."  Or, "My coffee tastes exponentially worse at this Starbucks as opposed to the one on Main Street."

I usually just smile and nod.  As if I understand what you're saying.

But, I really don't.

How do you know the change is exponential when you're only comparing two points?  How do you know it's not linear, perhaps with a steep slope?

To illustrate my point, let's say on Day 1 you rate your sleep as a 2.  On day 2, you rate your sleep as a 4. (I have no idea what these numbers indicate, but you must be able to rate your sleep on some kind of scale if you can make a statement like the aforementioned one.)  Well, then, maybe your sleep pattern, indeed, is following an exponential trend line:

An exponential function:  y=2^x

Or...you could have trend lines such as:

A linear function:  y=2x

A quadratic function:  y=(2/3)x^2+(4/3)

A logarithmic function:  y=2+2.88539ln(x)

And these only represent a few of the possibilities.

So, residents of the great Midwest:  I urge you--be more creative in your comparisons.  Don't assume you need to use the phrase "exponentially better."  Nay.  Why not try something like, "quadratically better," or "logarithmically better"?

Sincerely,

The Picky One