Before we go on to discuss exponential decay, we should pause and discuss some of the terms that are frequently used in these problems. First let's talk about the term factor.
Suppose you invested $100, and after a time, your investment was worth $300. The final value ($300) would be three (3) times the initial value. We would say that your investment had increased by a factor of 3.
On the other hand, if you made a poor investment, and the value decreased from $100 to $25, then the final value would be a quarter (1/4) of the initial value. We would say the investment had decreased by a factor of 4.
If a population of 500 increased by a factor of 1.5, then there would be a population of (500)(1.5) = 750. If the same population decreased from 500 by a factor of 1.5, then there would be 500/1.5 = 333 remaining.
When there is an increase, the ratio of the final number to the initial number is the factor. That is