   SEARCH HOME Math Central Quandaries & Queries  Question from william, a student: what is the difference between growth factor and growth rate? please reply soon!!!!!!! ps this is urgent We have two quite different responses for you because we don't believe the terms means the same thing to different people. You can probably tell when you read them which, if either, refers to what you are doing in class.

Hi William.

Growth factor is the factor by which a quantity multiplies itself over time.
Growth rate is the addend by which a quantity increases (or decreases) over time.

For example, compound interest is a growth factor situation: If your investment yields 10% annually, then that means that each year, your total has multiplied itself by 110% (the growth factor is 1.10).

Growth rate isn't expressed as a percentage. It is something that is constant such as "the height of this tree grows at the rate of 10 cm/year".

Here's a question for that shows you how growth factors and growth rates differ: My sister and I each have an allowance this week of $0.01 each. What happens if the growth factor of my sister's allowance is that it doubles every week? What happens if the growth rate of my allowance is that it increases by$10.00 each week?

next week, I get $10.01, my sister gets$0.02.
the following week, I get $20.01, my sister gets$0.04.

Who do you think will get more money this month?
Who do you think will get more money this year?

Cheers,
Stephen La Rocque.

Hi William,

I think both terms are referring to situations like the compound interest that Stephen mentions above, that is an exponential rate of growth. In his example the investment yields 10% annually. I would say the growth rate is 10% and the growth factor is 1.10. The growth rate is a percentage and the growth factor is a multiplying factor.

For example look at http://www.eckstein.seattleschools.org/rmohashi/DailySummary2.html

Harley     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.