How does exponential growth differ from linear growth?

1 Answer
Dec 26, 2014

With linear growth the same amount is added every period.
With exponential growth it is multiplied by the same factor every period.

Linear growth:
Say you make a very good $1000 investment, that pays out 10% every year. After one year you will have $1000 in the investment + $100 paid out, after 2 years you will have $1200, etc.

General formula:
N=current value
B=beginning value (start)
p=value to be added every period
t=number of periods

Exponental growth:
Same investment, only you don't cash in your $100 every year, but you re-invest under the same conditions. After one year there will be $1100 in your account, which will fetch $110 (10%) in the second year. So after the second year there will be $1100+$110=$1210, etc.
So the money grows by 10% plus 10% over that 10%, etc.
Or: The money gets multiplied by 1.10 every year (=100%+10%).
This value is called the growth factor abbreviated as #g#

General formula:
(other letters meaning the same as above)

Exponential growth models are used to describe a lot:
One example is the number of bacteria on your meat, where the growth factor is dependant mostly on temperature, and #t# is usually measured in hours.