Bird Population Growth Analysis

A research study analyzes the population growth of a certain species of birds in a protected area. The population, modeled by the quadratic function:

$$ P(t) = -4t^2 + 40t + 100 $$

represents the number of birds $ P $ after $ t $ years, where $ t $ is a non-negative integer. The maximum population occurs at the vertex of this parabola. Additionally, researchers anticipate that as the area becomes overly populated, the population will start to decline.

Based on the quadratic model, which of the following statements is true regarding the population of birds?