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how many calories in a large egg - Sourci

📅 May 1, 2026 👤 scraface

May 01, 2026

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📌 Question: In a biotechnology experiment, a bacterial culture grows such that the population $ P(t) $ after $ t $ hours is modeled by $ P(t) = P_0 \cdot e^{kt} $. If the population triples every 5 hours, how long will it take to grow from 200 to 16200 bacteria?

📌 We are given the exponential growth model:

📌 P(t) = P_0 \cdot e^{kt}

📌 We know that $ P(5) = 3P_0 $, so:

📌 3P_0 = P_0 \cdot e^{5k} \Rightarrow 3 = e^{5k}

📌 Take the natural logarithm of both sides:

📌 \ln(3) = 5k \Rightarrow k = \frac{\ln(3)}{5}

📌 Now, we find the time $ t $ such that $ P(t) = 16200 $ starting

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