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Question 611

The concentration of a cleaning agent, CCC grams per litre, in a mixing tank at time ttt minutes after the supply is activated is modelled by the differential equation

dCdt=R−0.15C \frac{dC}{dt} = R - 0.15C dtdC​=R−0.15C

where RRR is a constant. Initially, the tank contains pure water.

a.

Solve the differential equation to show that C=R0.15(1−e−0.15t)C = \frac{R}{0.15}(1 - e^{-0.15t})C=0.15R​(1−e−0.15t).

[5]
b.

In the long term, the concentration of the cleaning agent in the tank approaches 40 grams per litre.

Find the value of RRR.

[2]
c.

Find the time, in minutes, for the concentration to reach 25 grams per litre, giving your answer to 2 significant figures.

[3]
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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