Population growth does not follow exponential growth mainly because of limited resources. However, in laboratory environments populations can exhibit exponential growth. For example, bacteria populations grow incredibly fast because of their short reproductive times. In the article Exponential & Logistic Growth “we could start with just one bacterium and have enough bacteria to cover the Earth with a 1-foot layer in just 36 hours.”
In exponential growth models, the rate of growth in a population never changes and is typically unrealistic. In the real world resources like food, for example, will run out if a population keeps growing exponentially. Thus a population will reach its carrying capacity. Carrying Capacity is the maximum number of individuals a population can support based on that population’s needs.