A scientist is tracking the concentration of two specific catalysts in a chemical reaction chamber.
The concentration of the first catalyst, C1C_1C1 (in ppm), is modelled by the equation
C1=Aekt,t≥0 C_1 = A e^{kt}, \quad t \ge 0 C1=Aekt,t≥0where A A\,A and k k\,k are positive constants and t t\,t is the time in hours from the start of the reaction.
Given that:
Find the exact value of A A\,A and the value of k k\,k to 4 significant figures.
The concentration of the second catalyst, C2C_2C2 (in ppm), is modelled by the equation
C2=50000e−0.6t,t≥0 C_2 = 50000 e^{-0.6t}, \quad t \ge 0 C2=50000e−0.6t,t≥0where t t\,t is the time in hours from the start of the reaction.
Find the rate of decrease of the concentration of this second catalyst exactly 5 hours from the start. Give your answer to 3 significant figures.
At time t=Tt = Tt=T, the concentrations of the two catalysts are equal.
Find the value of TTT, giving your answer to 3 significant figures.
(Solutions relying entirely on calculator technology are not acceptable.)
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.
