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Home » f(3) = 4(3) - 5 = 12 - 5 = 7 - Tacotoon

f(3) = 4(3) - 5 = 12 - 5 = 7 - Tacotoon

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 First, model the data as an arithmetic sequence. The temperature increases from year 1 to 7 by 28.1 to 30.1 = 2.0°C over 6 intervals.

📌 Common difference: (30.1 − 28.1) / 6 = 2.0 / 6 = <<2.0/6=0.3333>>1/3°C per year

📌 From year 7 to year 10 is 3 more years: 3 × (1/3) = <<3*(1/3)=1.0>>1.0°C increase

📌 Predicted temperature: 30.1 + 1.0 = <<30.1+1.0=31.1>>31.1°C

📌 A linguist trains a transformer model on 3 billion words and observes perplexity at 45. If perplexity is defined as 2^H where H is the causal entropy in bits per word, what is the average entropy H per word in decimal form?

📌 Given: perplexity = 2^H = 45

📌 Take log₂: H = log₂(45) = ln(45)/ln(2) ≈ 3.8067 / 0.6931 ≈ <<3.8067/0.6931=5.492>>5.492

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