# Math Help - Radioactive Decay

If 80% of a radioactive element remains radioactive after 250 years, what percent remains radioactive after 600 years? What is the half life of the element?

2. Originally Posted by Neversh
If 80% of a radioactive element remains radioactive after 250 years, what percent remains radioactive after 600 years? What is the half life of the element?
we use the formula $A(t) = A_0e^{-rt}$

where $A(t)$ is the amount remaining after time $t$, $A_0$ is the initial amount, and $r$ is the decay constant.

say $A_0 = 1$, then when $t = 250$, we have

$0.8 = e^{-250r}$

use that equation to find $r$.

after that, you can answer the other questions (the half-life is easy, it is $\frac {\ln 2}r$)