A large reservoir is contaminated with a chemical pollutant. The concentration, PPP parts per billion (ppb), of the pollutant after ttt days of treatment can be modelled by
P=P0e−kt P = P_0 e^{-kt} P=P0e−ktwhere P0P_0P0 is the initial concentration and kkk is a positive constant. The model is considered accurate for high concentrations.
It takes 22.5 days for the concentration of the pollutant to reach 40% of its initial value.
Determine the number of weeks required for at least 97% of the original pollutant to be removed.
Find the percentage of the initial concentration remaining after 4 weeks. Give your answer to two significant figures.
Explain why the model can only provide an estimate for the actual concentration 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.
