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is it daylight savings now - Sourci

📅 April 30, 2026 👤 scraface

Apr 30, 2026

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📌 We know that \( P(200) = 2P_0 \), so:

📌 \( 2 = e^{200k} \Rightarrow k = \frac{\ln 2}{200} \)

📌 Now, we go 600 years before 1000 years ago, so 800 years before layer A:

📌 \( P(-800) = P_0 \cdot e^{(\ln 2 / 200)(-800)} = P_0 \cdot e^{-4\ln 2} = P_0 \cdot (e^{\ln 2})^{-4} = P_0 \cdot 2^{-4} = P_0 / 16 \)

📌 Given that current count (1000 years ago, t = 0) is 48, so \( P_0 = 48 \) (at t = 0 for layer A)

📌 But that’s the modern value. We want the count 600 years ago, i.e., at t = -600

📌 So: \( P(-600) = 48 \cdot e^{(\ln 2 / 200)(-600)} = 48 \cdot e^{-3\ln 2} = 48 \cdot 2^{-3} = 48 / 8 = 6 \)

📌 A hydrologist models the discharge of a river as a function of rainfall: \( Q = 50R^{0.7} \), where \( Q \) is discharge in m³/s and \( R \) is rainfall in cm. If rainfall increases from 30 cm to 40 cm, by how much does discharge increase? Round to the nearest whole number.

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