# How does exponential growth differ from linear growth?

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:
$N = B + p \cdot t$
Where
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:
$N = B \cdot {g}^{t}$
(other letters meaning the same as above)

Remark:
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.