A requirement for exponential growth in a population is that the population experiences continuous, unrestricted reproduction with a constant per capita growth rate over time. In other words, each individual in the population contributes equally to the rate of growth, and there are no limiting factors that constrain reproduction or survival.
In exponential growth, the population size increases at an accelerating rate, with the growth rate proportional to the current population size. This creates a feedback loop where a larger population leads to more individuals reproducing, resulting in even more population growth.
In reality, exponential growth is rarely sustained over extended periods because various factors, such as limited resources, predation, competition, and disease, typically impose constraints on population growth. Eventually, these limiting factors cause the population growth rate to slow down and reach a more stable state, which can be represented by a logistic growth model.