The population of a town increases by 3% every year. In the year 2000, the population was 3000. Find the population in the year 2003.

Analyze the question: The population grows by 3% each year, which is compound growth. We start in 2000 with 3000 people and need the population 3 years later, in 2003.

Concept: For compound growth,

A = P(1 + r/100)ⁿ

where P is the starting amount, r is the percentage rate, and n is the number of years.

Solution:

• P = 3000
• r = 3%
• n = 2003 − 2000 = 3 years

A = 3000 × (1.03)³

Calculate (1.03)³ step by step:

• 1.03² = 1.0609
• 1.0609 × 1.03 = 1.092727

A = 3000 × 1.092727 = 3278.18

So the population is about 3,278.

Check the year-by-year growth:

• 2001: 3000 × 1.03 = 3090
• 2002: 3090 × 1.03 = 3182.7
• 2003: 3182.7 × 1.03 = 3278.18 ✔

Option A (3,182) is the trap answer: it is the population after only 2 years.

Tip: Count the number of years by subtracting the dates (2003 − 2000 = 3). For "increase by r%" use the multiplier (1 + r/100), and for "decrease" use (1 − r/100). Always check whether an option matches an intermediate year, because examiners use those as distractors.