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Home » Subtract the second equation from the first: - 500apps

Subtract the second equation from the first: - 500apps

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 Question:** A deep sea microbiologist is studying the population growth of a chemosynthetic bacterium. The population \(P(t)\) at time \(t\) (in hours) follows the logistic growth model:

📌 P(t) = \frac{1000}{1 + 9e^{-0.5t}}

📌 Find the time \(t\) when the population reaches half of its carrying capacity.

📌 Solution:** The carrying capacity \(K\) of the logistic model is the maximum population, which is 1000 in this case. Half of the carrying capacity is \(500\). We set \(P(t) = 500\) and solve for \(t\):

📌 = \frac{1000}{1 + 9e^{-0.5t}}

📌 Multiply both sides by the denominator:

📌 500(1 + 9e^{-0.5t}) = 1000

📌 Divide both sides by 500:

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