A town grows 4% annually, but emigration reduces the population by 1/2% each year. What is the overall percentage increase over 3 years?

Introduction / Context: When two opposing percentage effects apply annually, combine them multiplicatively each year. Here, net annual growth equals +4% − 0.5% = +3.5%. Over multiple years, compound the net factor, not the separate components.

Given Data / Assumptions:

• Birth/immigration growth = +4% ⇒ factor 1.04.
• Emigration loss = −0.5% ⇒ factor 0.995.
• Net yearly factor = 1.04 * 0.995 = 1.035 (i.e., +3.5%).
• Time = 3 years.

Concept / Approach: Overall multiplier after 3 years = (1.035)^3. Convert the multiplier to a percent increase by subtracting 1 and multiplying by 100.

Step-by-Step Solution:

Verification / Alternative check: Log-based approximation: 3 * 3.5% = 10.5% plus a small compounding addition (~0.35%) gives ~10.85%, consistent.

Why Other Options Are Wrong: 9.8 and 10 neglect compounding; 10.5 uses 3 × 3.5% without compounding; 11.5 overshoots realistic compounding.

Common Pitfalls: Adding annual percentages linearly and ignoring multi-year compounding.

Final Answer: 10.8