CB.Calc.FUN-7.H: Interpret the meaning of the logistic growth model in context.

Interpret the meaning of the logistic growth model in context.

Example Problems

The number D(t) of e‑book downloads after t days satisfies the logistic differential equation:

\frac{dD}{dt} = \frac{2}{75} D \cdot (4500 - D)

where the initial number of downloads is

30

.

What is the carrying capacity of the download count?

The number R(t) of rabbits in a refuge after t months satisfies the logistic differential equation:

\frac{dR}{dt} = \frac{1}{25} R \cdot (500 - R)

where the initial number of rabbits is 30.

What is the carrying capacity of the rabbit population?

The number B(t) of bacteria in a petri dish after t hours satisfies the logistic differential equation:

\frac{dB}{dt} = 0.5 B \cdot \left(1.2 - \frac{B}{6000}\right)

where the initial number of bacteria is 120.

What is the number of bacteria when the population is growing the fastest?

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