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Home » 5) From Snoopy to Lucy: Dive Into Every Famous Character Name in Charlie Brown! - Baxtercollege

5) From Snoopy to Lucy: Dive Into Every Famous Character Name in Charlie Brown! - Baxtercollege

📅 March 11, 2026 👤 scraface

Mar 11, 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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z = e^{-2\pi i / 9},\ e^{-8\pi i / 9},\ e^{-14\pi i / 9} = e^{4\pi i /...
So the six roots are:
e^{2\pi i / 9},\ e^{8\pi i / 9},\ e^{14\pi i / 9},\ e^{-2\pi i / 9},\...
The imaginary part of $ e^{i\theta} $ is $ \sin \theta $. We compute $...
$ \sin(2\pi/9) = \sin(40^\circ) \approx 0.6428 $
$ \sin(8\pi/9) = \sin(160^\circ) = \sin(20^\circ) \approx 0.3420 $
$ \sin(14\pi/9) = \sin(280^\circ) = \sin(-80^\circ) = -\sin(80^\circ)...
$ \sin(-2\pi/9) = -\sin(40^\circ) $
$ \sin(-8\pi/9) = -\sin(40^\circ) $
$ \sin(4\pi/9) = \sin(80^\circ) \approx 0.9848 $

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