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Home » \[ V = \frac133 \pi hr^2 \] - Londonproperty

\[ V = \frac133 \pi hr^2 \] - Londonproperty

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 A hydrologist uses a groundwater model where water level drops exponentially: h(t) = h₀ × e^(−0.02t). If the initial level is 50 meters, what is the drop in water level after 25 years?

📌 h(25) = 50 × e^(−0.02×25) = 50 × e^(−0.5) ≈ 50 × 0.6065 = <<50*0.6065=30.325>>30.325 m. Drop = 50 − 30.325 = 19.675 m

📌 #### 19.675

📌 A science policy analyst compares two climate models: one predicts global temp rise of 0.2°C per decade; the other uses a quadratic trend T(t) = 0.15t² + 0.1t. What is the predicted difference in temperature after 50 years?

📌 Linear model: 0.2 × 5 = 1.0°C. Quadratic: 0.15×2500 + 0.1×50 = 375 + 5 = 380 → 38.0°C increase? No — units unclear. But assuming pre-industrial 15°C, predict:

📌 T₁ = 15 + 0.2×5 = 16.0°C. T₂ = 15 + 0.15×2500 + 0.1×50 = 15 + 375 + 5 = <<15+375+5=395>>395°C? Invalid.

📌 Reinterpret: only increase. ΔT₁ = 0.2×5 = 1.0°C. ΔT₂ = 0.15×(50²)/100? No. Use expression: T₂ = 0.15×(2500) + 0.1×50 = 375 + 5 = 380 → still invalid.

📌 Wait: likely t in years, T(t) in °C added. So T(50) = 0.15×(50)² + 0.1×50 = 0.15×2500 + 5 = 375 + 5 = 380 → absurd.

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