# What is the half life decay rate formula?

##### 1 Answer

If we start from an **initial concentration** of **final concentration**

Therefore, the first half-life is written as

To find *further* half-lives, keep *halving* the concentration

#[A] = [A]_0cdot1/2cdot1/2cdotcdotcdot#

or

#color(green)([A]= [A]_0(1/2)^n)#

If we want to determine the **number** of half-lives

So, we could write this in a more convenient form as

#color(green)([A]= [A]_0(1/2)^(t"/"t_"1/2"))#

Or, in a more universal form, since **quantity of the decaying substance as a function of time**

#color(blue)(N(t)= N_0(1/2)^(t"/"t_"1/2"))#

where