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- 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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