The concentration CCC mg/L of a specific industrial pollutant in a processing tank ttt hours after a chemical filtration process begins is modelled by the equation
C=C0e−kt C = C_0 e^{-kt} C=C0e−ktwhere C0C_0C0 is the initial concentration and kkk is a positive constant. The model is designed to represent the efficiency of the filtration over a long period.
It takes 10 hours for the concentration of the pollutant to reduce to 50%50\%50% of its initial value.
Determine the number of days required for the concentration to be reduced by at least 99%99\%99% from its initial value. Give your answer to one decimal place.
Determine the percentage of the initial concentration remaining in the tank after 6 days. Give your answer to two significant figures.
Explain why this model only provides an estimate for the actual concentration of the pollutant in the tank.
Explain why this model is physically unrealistic for the tank as t→∞t \to \inftyt→∞.
480 exam-style questions on AQA A Level Maths 1.11 H: Integration, 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). Each one has a worked solution and a mark scheme showing where the marks go.