O-LevelMathematicsAlgebra and graphs4024/22 · Oct/Nov 2025 · Q166 Marks
The population of a town decreases exponentially at a rate of x% per year. The population of the town on 1 January 2020 was 120000. The population of the town on 1 January 2023 was 102885.
- (a)Find the value of x.[3]
- (b)After 1 January 2023 the population of the town starts to increase exponentially at a rate of 1.6% per year. Find the year in which the population on 1 January first becomes more than 120000.[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.
- [3] 5. M2 for ³√(102885/120000) oe or M1 for 102885 = 120000×k³ oe
- [3] 2033 nfww. B2 for 10 [years] nfww or 9.6 to 9.7 or M2 for 102885×(1 + 1.6/100)ᵏ > 120000 oe or 102885×(1 + 1.6/100)⁹ oe or evaluates (1 + 1.6/100)⁹ or (1 + 1.6/100)¹⁰ and shows 1.166 or 1.1663 to 1.1664 or M1 for 102885×(1 + 1.6/100)ᵏ oe or for (1 - 5/100)³ × (1 + 1.6/100)ᵏ oe
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