# How does exponential growth differ from linear growth?

##### 1 Answer

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:

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

General formula:

(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