A population grows according to a logistic growth model, with population parameter$\lambda$= 4.0 and starting population fraction x = 0.7 for the first year. The value of x after the fourth year is:

Question

Quizplus · Accepted Answer

The logistic growth model is given by the formula $x_{n+1} = x_n + \lambda x_n(1 - x_n)$, where $x_n$ is the population fraction at year n, and $\lambda$ is the population parameter. Given $\lambda = 4.0$ and starting $x = 0.7$, we can calculate the population fraction for subsequent years. After the fourth year, the population fraction approaches 1, which is closest to choice D) 0.994. This is because, with a high growth rate ($\lambda = 4.0$) and starting near the carrying capacity (0.7), the population quickly approaches the model's limit.

A Population Grows According to a Logistic Growth Model, with Population