How do exponential growth and carrying capacity interact?

Exponential growth and carrying capacity interact primarily when the exponential growth function is used to model the growth of a population of a species in an ecosystem.

The carrying capacity of that species in the ecosystem is the maximum population of said species that the ecosystem can support indefinitely, given the available resources. Thus, carrying capacity somewhat plays the part of an upper limit to the exponential growth function used to model that population's growth in the environment.

Note that certain factors can temporarily push the population over the carrying capacity, such as an introduction of a substantial quantity of the species from an exterior source. However, this leads to depletion of resources in the ecosystem, typically resulting in a substantial decrease in the population fairly quickly and sometimes even lowering the carrying capacity as a result (i.e. resources have been depleted so greatly that they will not recover to previous levels).

Exponential growth occurs when a population increases at a constant rate over a period of time, resulting in a J-shaped curve on a graph. Carrying capacity refers to the maximum population size that an environment can sustain indefinitely. When a population grows exponentially, it will eventually reach the carrying capacity of its environment. At this point, the population growth rate will slow down and eventually stabilize, as limited resources prevent further exponential growth. The interaction between exponential growth and carrying capacity is crucial in understanding population dynamics and ecological systems.