Hi Lisa,

If you have a plant that is growing one quarter inch per day then the growth rate is constant. Regardless of how tall the plant is on any particular day it will be on quarter inch longer the next day. Some things grow according to a different law. The amount they grow on any particular day depends on how big they are on that day. Here is an example. In this example a colony of bacteria doubles in size every half hour. As you can see in this example the number of bacteria in the colony n half hours after the colony started growing is 2ⁿ. The fact that this expression is an exponential leads us to call this growth pattern exponential growth.

Her is another example where the growth is negative, that is the size is decreasing. You just won $64,000 and you decide to give it away. One way is to decide on a charity every day and give the charity $1,000. In this model the amount of money you have is decreasing at a constant rate, $1,000 per day. After 64 days your money is gone. Another way to distribute your money is to give 1/4 of your money to a charity on the first day. On the second day give 1/4 of what is left to another charity. On day three give 1/4 of what is left to a third charity and so on. Hence

on day 1 you give away 1/4 × $64,000 and are left with 3/4 × $64,000
on day 2 you give away 1/4 × (3/4 × $64,000) and are left with 3/4 × 3/4 × $64,000 = (3/4)² × $64,000
on day 3 you give away 1/4 × ((3/4)² × $64,000) and are left with 3/4 × (3/4)² × $64,000 = (3/4)³ × $64,000
on day 4 you give away 1/4 × ((3/4)³ × $64,000) and are left with 3/4 × (3/4)³ × $64,000 = (3/4)⁴ × $64,000

Again you see that this is an exponential "growth" pattern, sometimes called exponential decay.

I hope this helps,
Penny