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11.11 Modelling with Differential Equations

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Question 20

The concentration, CCC mg/L, of a particular chemical residue in a large processing tank, ttt hours after a neutralising catalyst is introduced, is modelled by the differential equation

dCdt=−k(C−10)2 \frac{\text{d}C}{\text{d}t} = -k(C - 10)^2 dtdC​=−k(C−10)2

where kkk is a constant and C>10C > 10C>10.

Given that the concentration of the residue:

  • is 610610610 mg/L at the instant the catalyst is added
  • is 110110110 mg/L exactly 222 hours after the catalyst is added
a.

Solve the differential equation to show that, according to the model

C=at+bct+d C = \frac{at + b}{ct + d} C=ct+dat+b​

where a,b,ca, b, ca,b,c and ddd are integers to be found.

[6]
b.

Hence find, according to the model, the time taken for the concentration of the residue to fall to 404040 mg/L. Give your answer to the nearest hour.

[2]

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.

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