Difficulty: Easy
Correct Answer: 163098
Explanation:
Introduction / Context:
Successive percentage growth requires compounding, not addition. This population problem asks for the current value after three different annual growth rates are applied in sequence.
Given Data / Assumptions:
Initial population (3 years ago) = 150,000. Yearly growth factors: 1.02, then 1.025, then 1.04.
Concept / Approach:
Present population = 150,000 * 1.02 * 1.025 * 1.04. Multiply in order (multiplication is commutative) and avoid premature rounding to maintain accuracy. The final should be an integer in this crafted example.
Step-by-Step Solution:
Verification / Alternative check:
Combined factor: 1.02 * 1.025 * 1.04 = 1.08732; 150,000 * 1.08732 = 163,098.
Why Other Options Are Wrong:
Other values are near but reflect rounding or additive methods (2 + 2.5 + 4 = 8.5%), which is incorrect for successive growth.
Common Pitfalls:
Adding percentages directly or rounding after each step too aggressively. Use factors and keep precision to the end.
Final Answer:
163098
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