Number 4

4 marks · Normal

In 2018, the population of a town was 9,000 people. Every year, the population decreases by 2%.

(a)

Calculate the population after 3 years. Give your answer to the nearest whole number.

[3 marks]

(b)

Explain in one sentence why the answer is less than 9,000.

[1 mark]

Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.

Show answer

(a) 8,648

(b) A 2% decrease reduces the population each year, so the population gets smaller each time.

Common mistakes: uses simple subtraction instead of a multiplying factor

Show mark scheme and worked solution

Marking points

M1 (a) · 1 mark · Applies correct multiplying factor (0.98) or equivalent

M2 (a) · 1 mark · Raises to the correct power (3 years)

A1 (a) · 1 mark · Correct answer to nearest whole number

B1 (b) · 1 mark · Clear explanation for decrease

Worked solution

a) 9,000 × (0.98)^3 = 9,000 × 0.941192 = 8,648 (nearest whole number)

b) Each year, the population gets 2% smaller, so it gradually decreases.