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→∞.
Practise AQA A Level Maths 1.11 H: Integration with exam-style questions for A Level Maths. 436 questions covering 1.11.1 Fundamental Theorem of Calculus, 1.11.2 Integrating standard functions, 1.11.3 Definite integrals and areas, 1.11.4 Integration as the limit of a sum (A-level only), 1.11.5 Integration by substitution and by parts (A-level only), 1.11.6 Integration using partial fractions (A-level only), 1.11.7 Differential equations with separable variables (A-level only), and 1.11.8 Interpreting solutions of differential equations (A-level only), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
