The mass, M M\,M grams, of a radioactive isotope in a laboratory sample after t t\,t hours can be modelled by
M=M0e−kt M = M_0 e^{-kt} M=M0e−ktwhere M0 M_0\,M0 is the initial mass and k k\,k is a positive constant. The model remains valid for large masses.
It takes 12.4 hours for the mass of the sample to reach 50% of its initial value.
Determine the number of days required for at least 95% of the mass of the original sample to decay.
Find the percentage of the initial mass remaining after 5 days. Give your answer to two significant figures.
Explain why the model can only provide an estimate for the actual mass observed.
Explain why the model is invalid in the very long run as t→∞t \to \inftyt→∞.
