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Home » $6\binom86 = 6 \cdot 28 = 168$ - Coaching Toolbox

$6\binom86 = 6 \cdot 28 = 168$ - Coaching Toolbox

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 A deep-sea extremophile genomics researcher is studying the growth dynamics of microbial communities near hydrothermal vents. The population of a certain microbial species is modeled by the equation \( P(t) = P_0 e^{kt} \), where \( k \) is a growth constant. If the population triples in 5 hours, what is the value of \( k \)?

📌 We are given the population model

📌 \[ P(t) = P_0 e^{kt}, \]

📌 and that the population triples in 5 hours, so

📌 \[ P(5) = 3P_0. \]

📌 Substitute into the equation:

📌 \[ 3P_0 = P_0 e^{5k}. \]

📌 Divide both sides by \( P_0 \):

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