Problem 10 · 2024 AMC 8
Easy
Ratios, Rates & Proportions
unit-ratelinear-extrapolation
In January 1980 the Mauna Loa Observatory recorded carbon dioxide CO2 levels of 338 ppm (parts per million). Over the years the average CO2 reading has increased by about 1.515 ppm each year. What is the expected CO2 level in ppm in January 2030? Round your answer to the nearest integer.
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Answer: B — 414 ppm.
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Hint 1 of 2
"Same amount every year" is the signal for one move: total rise = rate × number of years. Don't add year by year.
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Hint 2 of 2
Technique — linear growth: increase = (yearly rate) × (years elapsed), then add to the starting level. Count the years from 1980 to 2030 first.
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Approach: rate × time, then add to start
- A constant yearly increase means the rise is just rate × time — no need to step through 50 separate years. Years elapsed: 2030 − 1980 = 50.
- Total increase: 50 × 1.515 = 75.75 ≈ 76 ppm.
- New level: 338 + 76 = 414. Sanity check: ~1.5 ppm/yr over 50 years is roughly 75, landing just above 338+75 = 413 — only 414 is in range, so estimation alone nails the choice.
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