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Question 185

The pressure, PPP kPa, inside a leaking decompression chamber ttt minutes after the leak is first detected, is modelled by the differential equation

dPdt=−k(P−100)2 \frac{\text{d}P}{\text{d}t} = -k(P - 100)^2 dtdP​=−k(P−100)2

where kkk is a positive constant and P>100P > 100P>100.

Given that the pressure in the chamber:

  • is 110011001100 kPa at the instant the leak is detected
  • is 350350350 kPa exactly 101010 minutes later
a.

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

P=at+bct+d P = \frac{at + b}{ct + d} P=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 pressure in the chamber to reach 150150150 kPa. Give your answer to the nearest minute.

[3]

Integration Questions

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

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.

Question bank