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CAIE A-Level Mathematics A2 3.8.4 Differential Equations Questions

Practise interpreting differential-equation models, long-term behaviour and parameter effects.

Syllabus
2028–2030
Course
Mathematics 9709
Level
A2

Exam points

  • interpret solutions and long-term behaviour of differential-equation models
  • use derivatives and limits to analyse model predictions
  • relate model parameters and initial conditions to context

CAIE A-Level Mathematics A2 3.8.4 Differential Equations Questions question 1

[Maximum number: 1]

A large plantation of area 20 km220 \mathrm{~km}^{2} is becoming infected with a plant disease. At time t years the area infected is x km2x \mathrm{~km}^{2} and the rate of increase of x is proportional to the ratio of the area infected to the area not yet infected.

When t=0, x=1 and dx dt=1\frac{\mathrm{d} x}{\mathrm{~d} t}=1.

Calculate the value of t at which the entire plantation becomes infected.

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