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Case study·Hard exam skill (4/5)·No calculatorNeeds mentor review

Difficulty guide

The label describes the problem, not your ability.

1/5 - Foundational

Warm-up setup; checks one basic idea.

2/5 - Routine exam skill

Normal syllabus skill; usually one main rule or interpretation.

3/5 - Standard multi-step

Exam-style problem with multiple steps or a common trap.

4/5 - Hard exam skill

High-end exam problem; combines methods carefully.

5/5 - Challenge

Stretch problem beyond normal exam pressure.

Question

The rate of growth of a culture is proportional to its current size. Let N(t)N(t) be the size at time t,t, so dNdt=kN\frac{dN}{dt}=kN and N(0)=N0.N(0)=N_0.
Total: 4 marks

(a) Separate the variables. (1 mark)

(b) Find the general solution in terms of N0N_0. (2 marks)

(c) If k>0k>0, state whether the culture is growing or decaying. (1 mark)

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cbse-math-12.u3.t3-10.case.005

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