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.
363 exam-style questions on CCEA A Level Maths 3.6 Integration (A-level only), covering 3.6.1 Integration (A-level only), 3.6.2 Integration (A-level only), 3.6.3 Integration (A-level only), 3.6.4 Integration (A-level only), 3.6.5 Integration (A-level only), 3.6.6 Integration (A-level only), and 3.6.7 Integration (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.