Problem 15 · 1998 AJHSME
Medium
Ratios, Rates & Proportions
exponential-growthestimation
Nisos Isles. In 1998 the islands have 200 people, and the population triples every 25 years. Estimate the population in the year 2050.
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Answer: D — About 2000.
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Hint 1 of 2
'Triples every 25 years' means the clock matters, not a formula. How many full 25-year steps fit between 1998 and 2050? Each step multiplies the people by 3.
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Hint 2 of 2
Two steps means multiply by 3, then by 3 again — don't add the steps, stack the triplings.
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Approach: count the 25-year steps, multiply by 3 for each
- From 1998, the tripling moments land at 2023 (one step) and 2048 (two steps) — and 2048 is essentially 2050. So two full triplings have happened.
- Each tripling is a ×3: 200 → 600 → 1800. (Growth multiplies, it doesn't add — that's the whole flavor of these problems.)
- 1800 is closest to 2000.
- Why this transfers: for repeated-multiplying growth, count how many doubling/tripling periods have passed, then multiply that many times. Adding the periods instead of multiplying is the classic mistake.
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