4024/21 Oct/Nov 2025, Question 14: Exponential growth
Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 3 marks
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The question, in short
A population of 5.4 million grows by 3.6% each year. How many complete years until it reaches 8 million?
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 3 marks
- 1Population after n years = 5.4 × (1 + 3.6/100)ⁿ = 5.4 × 1.036ⁿ
- 2After 11 years: 5.4 × 1.036¹¹ = 7.968… million (less than 8)
- 3After 12 years: 5.4 × 1.036¹² = 8.254… million (more than 8)
- 4Number of complete years = 12
Answer12
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