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Home » You Won’t Believe What This LookA-Horse Pro Reveals About Sea Horse Intelligence! - Carbonext

You Won’t Believe What This LookA-Horse Pro Reveals About Sea Horse Intelligence! - Carbonext

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 Question: An ichthyologist observes that the population of a rare fish species in the Amazon doubles every 3 years. If the current population is 324 and it started at a power of 3, what is the smallest exponent \( k \) such that the population reaches at least \( 3^k \)?

📌 Solution: The population grows as \( 324 \times 2^{t/3} \), where \( t \) is time in years. We want the smallest \( k \) such that:

📌 \times 2^{t/3} \geq 3^k

📌 But since we are to express the population as a power of 3, note that 324 = \( 3^4 \times 4 = 81 \times 4 = 2^2 \cdot 3^4 \). So:

📌 \text{Population} = 2^2 \cdot 3^4 \cdot 2^{t/3} = 2^{2 + t/3} \cdot 3^4

📌 For the population to be at least \( 3^k \), we need:

📌 3^4 \cdot 2^{2 + t/3} \geq 3^k \implies 2^{2 + t/3} \geq 3^{k - 4}

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