An environmental engineer is monitoring the reduction of a hazardous chemical in a decontamination tank. The concentration of the chemical, C C\,C ppm (parts per million), at time t t\,t hours after the process starts is modeled by the equation
C=C0e−kt C = C_0 e^{-kt} C=C0e−ktwhere C0 C_0\,C0 is the initial concentration and k k\,k is a constant related to the efficiency of the filtration system.
Experiments show that the time taken for the concentration of this chemical to reduce to half its previous value is 3.2 hours.
At 8:00 am, the initial concentration of the chemical in the tank is measured at 800 ppm.
Determine the estimated concentration of the chemical in the tank at 2:00 pm on the same day.
The tank requires a maintenance injection that will increase the concentration by exactly 600 ppm. Safety protocols dictate that the total concentration must never exceed 750 ppm. Find the earliest time that the maintenance injection can be administered. Give your answer to the nearest minute.
State one reason why the concentration predicted by this model might differ from actual measurements taken from the tank.
Practise Edexcel A Level Maths Integration with exam-style questions for A Level Maths. 437 questions covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations, matched to the Edexcel A Level Maths (9MA0) 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.
