Question

The logistic growth model P(t) = 1 + 30.29e^(-0.3594t) represents the population (in grams) of a bacterium after t hours. Determine the carrying capacity of the environment.

A) 30.29 g
B) 1 g
C) 0.3594 g
D) Infinite g

Answer 1

The carrying capacity in this logistic growth model is 31.29 grams, the sum of the constant terms in the equation.

Step-by-step explanation:

The carrying capacity in a logistic growth model represents the maximum population size that a particular environment can support indefinitely. In the given logistic growth model, P(t) = 1 + 30.29e-0.3594t, the carrying capacity is represented by the constant term that remains when the population growth rate levels off. As time t approaches infinity, the exponential part of the equation e-0.3594t approaches 0 and does not contribute to the population size, meaning that the carrying capacity is the remaining term, which is 1 + 30.29. Therefore, the carrying capacity of the environment is the sum of these two numbers, which equals 31.29 grams.