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"?
The Picky One