A researcher is monitoring the concentration of a specialized catalyst, PPP mg/L, within a chemical bioreactor. The concentration ttt minutes after the reaction commences is modelled by the equation
P=480e0.12t2e0.12t+3,t≥0, t∈R P = \frac{480e^{0.12t}}{2e^{0.12t} + 3}, \quad t \ge 0, \ t \in \mathbb{R} P=2e0.12t+3480e0.12t,t≥0, t∈RAccording to this model:
Determine the concentration of the catalyst at the instant the reaction begins.
Calculate the time ttt at which the concentration reaches 160 mg/L, giving your answer to 2 decimal places.
Explain why, according to this model, the concentration of the catalyst can never reach 250 mg/L.
Practise AQA A Level Maths 1.12 I: Numerical methods (A-level only) with exam-style questions for A Level Maths. 107 questions covering 1.12.1 Locating roots by change of sign (A-level only), 1.12.2 Iterative methods and Newton-Raphson (A-level only), 1.12.3 Numerical integration (A-level only), and 1.12.4 Numerical methods in context (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.
