The half-life of cobalt 60 is 5 years. How do you obtain an exponential decay model for cobalt 60 in the form Q(t) = Q0e^−kt?
We set up a differential equation. We know that the rate of change of the cobalt is proportional to the amount of cobalt present. We also know that it is a decay model, so there will be a negative sign:
This is a nice, easy and seperable diff eq:
Raise each side to exponentials:
Now that we know the general form, we need to work out what
Let half life be denoted by
Take natural logs of both sides:
For tidiness, rewrite