These two exercises are meant to give you practice in calculating the parameters
associated with radioactive decay. This is a two variable problem involving
the time which has elapsed and the remaining fraction. If you know either
one you can calculate the other. In the first exercise you are given the
time and are asked to calculate the remaining fraction. In the second you
are given the remaining fraction and are asked to calculate the remaining
time. In both cases you can check your answers against the computer, which
will respond by telling you if you got the answer correct, or if not, what
the correct answer should be. You can also elect to try a new problem,
either using the same isotope, or by selecting a different isotope with
a new half life.
Formulae
Both of these problems rely on the same formula. However it looks a little
different depending on whether you are given the time and are asked to
calculate the remaining fraction, or whether you are given the remaining
fraction and are asked to calculate the remaining time.
If you are given the time then you can calculate the remaining fraction
by setting y = N/N_{o} = e^{-kt}.
If you are given the remaining fraction then you can calculate the time
by setting x = -kt = ln(y)
In both cases you also need to calculate the decay constant k. Its value
in both cases is ln(2)/T, where T is the half life.