Question

the half life of a certain radioactive material= 76 hrs. An initial amount of the material has a mass of 794 kg. write an exponential function that models the decay.

Answer 1

Half Life Formula
\[A=A_0e^{\text{rt}}\]

Answer 2

Since it is half life, we know that final is half of the original
\[\frac{1}{2}=e^{\text{rt}}\]
\[\frac{1}{2}=e^{\text{76 r}}\]

Answer 3

So we take ln of both side leaving us with
ln(.5)=76r

Answer 4

Once you find what 'r' is
you can rewrite the equaion