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Home » If the sum of the first \(n\) natural numbers is 210, find \(n\). - Abbey Badges

If the sum of the first \(n\) natural numbers is 210, find \(n\). - Abbey Badges

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 A city’s population grows exponentially, doubling every 25 years. If the population was 500,000 in 2000, what will it be in 2100?

📌 From 2000 to 2100 is 100 years, or 4 doubling periods. Population = 500,000 × 2⁴ = 500,000 × 16 = 8,000,000.

📌 To analyze vegetation cover, a GIS analyst calculates that a forested area decreased from 1,500 hectares to 900 hectares over 12 years. What is the average annual percentage decrease in forest area?

📌 Total decrease = 1,500 − 900 = 600 hectares. Fractional decrease = 600 ÷ 1,500 = 0.4. Over 12 years, average annual fractional decrease ≈ 0.4^(1/12) ≈ 0.971 (using continuous approximation). For percentage: (1 − 0.971)^(12) ≈ 0.4, so annual decay ≈ 1 − 0.971 = 0.029 → 2.9% per year.

📌 The atmospheric concentration of a greenhouse gas increases from 420 ppm to 450 ppm over 15 years. What is the average annual rate of increase in ppm per year?

📌 Total increase = 450 − 420 = 30 ppm. Over 15 years, average rate = 30 ÷ 15 = 2 ppm per year.

📌 A satellite dataset shows sea surface temperatures rising linearly from 25.4°C in 1990 to 26.8°C in 2020. What will the temperature be in 2050 if the trend continues?

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