The situation where a quantity is multiplied by a certain number every time step is
called exponential growth. This number
`g`
is called the growth rate and corresponds to the unit of time:
`g>0`
.
To determine whether a quantity grows exponentially, you compute the ratio of consecutive values. If these ratios
are (approximately) equal, you are dealing with exponential growth. The quantity then grows like this:
At the initial value is .
At you have .
At you have .
At you have .
So the formula applies .
When working with exponential growth you use powers: when you multiply the same number `g` times, you write . This is a power, where the growth rate is called the base and is called the exponent.
An example of exponential growth is growth or decay with a fixed percentage. When the growth is percent, the growth rate is: . When the quantity increases and `g>1` : exponential growth. When the quantity decreases and `g < 1` (but greater than 0): exponential decay.