Population with opposite successive changes: Town population = 126800. It increases by 15% in the first year and decreases by 20% in the second year. What is the population after 2 years?

Introduction / Context:
Successive percent changes multiply, not add. We apply the 15% increase then the 20% decrease to the base 126800.

Given Data / Assumptions:

• Initial population = 126800.
• Year 1 factor = 1.15.
• Year 2 factor = 0.80.

Concept / Approach:
Final population = 126800 * 1.15 * 0.80 = 126800 * 0.92.

Step-by-Step Solution:

Verification / Alternative check:
Increase by 15%: 126800 → 145820; then decrease by 20%: 145820 * 0.8 = 116656. Both methods agree.

Why Other Options Are Wrong:

• Other values do not match the exact factor 0.92 applied to 126800.

Common Pitfalls:
Adding −20% and +15% to get −5% and multiplying once; this ignores compounding on different bases.

Final Answer:
116656