An industrial chemist is monitoring the concentration of a catalyst, CCC mg/L, in a pressurized chemical reactor. The concentration at time ttt minutes after the reaction begins is modelled by the equation
C=150λe0.15tλe0.15t+12C = \frac{150 \lambda e^{0.15t}}{\lambda e^{0.15t} + 12}C=λe0.15t+12150λe0.15t
where λ\lambdaλ is a positive constant.
Given that:
Show that λ=3\lambda = 3λ=3.
Calculate the value of TTT, giving your answer to one decimal place. (Solutions relying entirely on graphical or numerical methods are not acceptable.)
Determine, according to this model, the maximum possible concentration of the catalyst as time increases.
Practise Edexcel A Level Maths 10.4 Applications to Modelling with exam-style questions for A Level Maths. 5 questions, 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.