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Home » What ‘a_r’ Means for Your Future – Experts Reveal the Untold Secrets! - Dyverse

What ‘a_r’ Means for Your Future – Experts Reveal the Untold Secrets! - Dyverse

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 A biologist is studying a population of beetles whose growth rate follows a cubic function \( f(x) = ax^3 + bx^2 + cx + d \). Observations show \( f(1) = 4 \), \( f(2) = 15 \), \( f(3) = 40 \), and \( f(4) = 85 \). Determine the coefficients \( a \), \( b \), \( c \), and \( d \).

📌 We solve the system from:

📌 \( a + b + c + d = 4 \)

📌 \( 8a + 4b + 2c + d = 15 \)

📌 \( 27a + 9b + 3c + d = 40 \)

📌 \( 64a + 16b + 4c + d = 85 \)

📌 Subtract (1) from (2):

📌 \[ (8a + 4b + 2c + d) - (a + b + c + d) = 15 - 4 \]

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