F.LE.A.1.d: Distinguish between situations that can be modeled with exponential functions and logistic functions.

Distinguish between situations that can be modeled with exponential functions and logistic functions.

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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