Have you ever heard the expression: “Wow, that increased exponentially!”? This phrase captures the essence of exponents. When a positive number greater than 1 increases exponentially, it does not merely increase; it increases a whole lot in a short amount of time.
An important property of exponents is that the greater the exponent, the faster the rate of increase. Consider the following progression:
| 51 = 5 52 = 25 53 = 125 54 = 625 |
Increased by 20 Increased by 100 Increased by 500 |
The important thing to remember is that for positive bases bigger than 1, the greater the exponent, the faster the rate of increase.