Radioactivity can be defined using this model:

, where

is the current amount of the substance

is the initial amount of the substance

is the decay constant

is the length of time

Now, we are told that we have after 1 year.

Thus,

Solving for k, we see that

Now, we can find the half life:

Half life is defined as , where

is the half life

is the decay constant

Thus,

Now, our decay model is

Can you find when ?

--Chris