Question

The logistic growth function f(t) = 720/1 + 8.0e-0.13, describes the population of a species of butterflies t months after they are introduced to a non- threatening habitat. how many butterflies were initially introduced to the habitat?

Answer 1

To determine the initial population of butterflies, evaluate the logistic growth function at t = 0. The initial population is the function's value at this point, which is 80 butterflies.

Step-by-step explanation:

The question refers to a logistic growth function that models the population of butterflies over time. To find how many butterflies were initially introduced to the habitat, we'll evaluate the function at t = 0, which represents the initial time. The function is given by:

f(t) = 720/(1 + 8.0e-0.13t).

At t = 0, the exponential term e-0.13(0) becomes e0 which equals 1. Substituting this into the function:

f(0) = 720/(1 + 8.0 * 1),

f(0) = 720/(1 + 8.0),

f(0) = 720/9,

f(0) = 80.

Therefore, 80 butterflies were initially introduced to the habitat.