# What do exponential growth and decay have in common?

Mar 30, 2015

They both work with the same equation: $N = B \cdot {g}^{t}$
Where
$N =$ new situation
$B =$ begin
$g =$ growth factor
$t =$ time

If the growth-factor is greater than $1$, then we have a growth.
If it is less than $1$ we call it decay.
(if $g = 1$ nothing happens, a stable situation)

Examples:
(1) A population of squirrels, starting at 100, grows by 10% every year. Then $g = 1.10$ and the equation becomes: $N = 100 \cdot {1.10}^{t}$ with $t$ in years.
(2) A radio-active material with original activity of 100, decays by 10% per day. Then $g = 0.90$ (because after a day only 90% will be left) and the equation will be: $N = 100 \cdot {0.90}^{t}$ with $t$ in days.