Here, we will model a population \( g(t) \) in an environment having carrying capacity \( A \). The population follows the model
$$ \begin{equation} \tag{11} g'(t) = \alpha g(t)(A - g(t)) \end{equation} $$where \( g(0) = g_0 \).
In this example, we let \( \alpha = 2 \), \( A = 1 \), and \( g_0 = 1.2 \).