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\frac12604368 = \frac105364 - High Altitude Science

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 In a sustainable forest project, the tree density increases by 8% per year. If the current density is 320 trees per hectare, in how many years will it exceed 500 trees per hectare? Use logarithms.

📌 Use: \( 320 \cdot (1.08)^t > 500 \)

📌 Divide: \( (1.08)^t > 500 / 320 = 1.5625 \)

📌 Take ln: \( t \ln(1.08) > \ln(1.5625) \)

📌 \( t > \frac{\ln(1.5625)}{\ln(1.08)} \approx \frac{0.4447}{0.07696} \approx 5.78 \)

📌 So, after 6 full years, density exceeds 500.

📌 A palynologist uses a regression model to estimate ancient rainfall \( R \) from pollen ratios: \( R = 2.5P - 15 \), where \( P \) is a standardized pollen index. If the correlation between \( P \) and \( R \) improves, reducing the error margin by 20%, and originally the standard error was 3.75 mm, what is the new standard error? Also, if the original 95% confidence interval was ±7.5 mm, what is the new width?

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