Exponential growth of a population is when the amount being added to the system is proportional to the amount already present; so the bigger the system, the greater the increase. The growth is limited only by the time it takes for the population to reproduce. Logistic growth, however, is when the growth rate decreases as the population reaches carrying capacity. Conditions where a population would exhibit exponential growth are for there to be unlimited resources (such as food and space) and no competition from other organisms. Exponential growth can't be sustained indefinitely because carrying capacity is eventually reached; in other words, resources are limited and eventually the max population an environment can sustain is reached.
Work Step by Step
Exponential growth is unrestrained by anything but the population's capacity to reproduce, and Logistic growth is growth that declines as the population reaches carrying capacity. Exponential growth must have unlimited resources and no competition; however, resources are limited, so a population can't sustain exponential growth forever.