For an annual rate of change of –31%, how do you find the corresponding growth or decay factor?
Let's say I start with $100. Then after one year, I will have lost $31 and therefore will have $100 - $31 = $69 left. This means that I get to keep 69% of my initial money.
To figure out how much money I will have the following year, we can imagine each of my dollars. I therefore get to keep 69 cents from every dollar. So I have
At this point, it is clear that every year my money multiplies by 0.69. This is what we call out decay factor.