Exponential vs logistic growth

Notice that the X-axis for population growth graphs is always "time." Time is the independent variable. Time may range from hours to decades, depending on the how quickly a new generation occurs. Bacteria populations, for instance, can reproduce in a matter of hours.

Notice that the Y-axis is the population size, which is the dependent variable. Population size is often the number of individuals in a population but is sometimes biomass instead.

The population eventually reaches a carrying capacity, which is the population size that can be sustained over time in a given environment. The carrying capacity varies population to population and can also change over time as the environment changes. In nature, populations often overshoot and then undershoot the carrying capacity before eventually stabilizing at the carrying capacity.

The logistic growth model is an S-shaped curve. At first, it increases rapidly, just like the exponential model, but as resources start to become limited, the population's rate of increase drops (this means that the population is still increasing in size but not as much as before). Eventually, the population stabilizes at its carrying capacity

The exponential model is a J-shaped curve, illustrating how the population continuously increases in size. Resources are unlimited, allowing the population to exponentially increase. This can happen in nature, but is only temporary- eventually the population is impacted by a limtation in resources.