A sample of a radioactive substance decayed to 91.5% of its original amount after a year. What is the half life of the substance? Also have to find the amount of time for it to decay to 30% of the original amount.
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