Skip to content
MathsGenie logo
Open app

Course home

  1. A Level
  3. Maths Edexcel
  5. Question bank

11.11 Modelling with Differential Equations

MediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142
Question 22

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]

11.11 Modelling with Differential Equations Questions

  1. A Level
  2. /Maths
  3. /11.11 Modelling with Differential Equations

Practise Edexcel A Level Maths 11.11 Modelling with Differential Equations with exam-style questions for A Level Maths. 51 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.

Question bank