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📅 April 30, 2026 👤 scraface

Apr 30, 2026

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📌 A glacier retreated 1,200 meters over 40 years. If the retreat rate doubled after the first 20 years, how many meters did it retreat in the second 20 years?

📌 Let the initial rate be r m/year. In the first 20 years, it retreated 20r meters. In the next 20 years, the rate was 2r, so it retreated 20 × 2r = 40r meters. Total retreat: 20r + 40r = 60r = 1,200 meters. Solving for r: r = 20. Retreat in second 20 years: 40 × 20 = 800 meters.

📌 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.

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