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Question 627

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≥0

where 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:

  • the concentration of the first catalyst was 500 ppm at the start of the reaction
  • the concentration was 2500 ppm after 4 hours
a.

Find the exact value of A A\,A and the value of k k\,k to 4 significant figures.

[4]
b.

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≥0

where 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.

[3]
c.

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.)

[4]
Markscheme

Integration Questions

  1. A Level
  2. /Maths
  3. /Integration

864 exam-style questions on Edexcel A Level Maths Integration, 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. Each one has a worked solution and a mark scheme showing where the marks go.

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