The logistic model is a mathematical representation used to describe how a population grows over time. It is particularly useful for modeling situations where growth is limited by factors such as resources or space. The model produces an S-shaped curve, known as the logistic curve, which starts with exponential growth, slows down as it approaches a maximum capacity, and eventually levels off. In the logistic model, the growth rate decreases as the population reaches its carrying capacity, denoted as K. The equation incorporates parameters like the initial population size and the growth rate, allowing researchers to predict future population dynamics in various fields, including ecology and economics.