Logarithms and Exponential Functions
Exponential Growth and Decay
Sometimes we wonder how Expo got to be so big, so quickly. Some celebrity stars fall as quickly as they rise, like those one-hit wonders out there that everybody feels a little awkward mentioning. Even Expo might be here today, gone tomorrow. What makes all the difference between whether Expo grows or shrinks is his little ol' base.
Why is that? Remember that exponential functions multiply their base by itself a number of times. This "number of times" is equal to the exponent. If we compare b > 1 and b < 1:
It's starting to seem like the base is the source of all of Expo's power, kind of like a horcrux. If that's the case, then he's an evil, immortal wizard who will stop at nothing to become the most powerful being in the universe. Could it be that Expo is really He-Who-Must-Not-Be-Named? If so, you've got to be prepared to face him.