How does carrying capacity affect exponential growth?
Carrying capacity typically acts as an upper limit upon an exponential growth function. Without outside circumstances to cause changes in parameters, an exponential growth function used to represent population growth in a natural environment will not surpass the carrying capacity; thus, the carrying capacity serves as a horizontal asymptote.
Carrying capacity is the maximum sustainable population of a given species in an environment, given the resources present in that environment. Note that this is the maximum sustainable population; with certain circumstances (massive influx of more members of the species from outside the environment, or rarely certain natural cyclic variations) the population can surpass the carrying capacity. However, the population will experience a sharp decline or "population crash" afterwards due to scarcity of resources.
For example, assume that in a given environment, the carrying capacity for deer is 1500. This means that the environment can sustain 1500 deer indefinitely with its available resources. For the moment, assume that our deer population begins at 1200 specimens.
Suppose further that, due to outside factors (increased predator activity, scarcity of resources), a population of 400 deer from a nearby environment migrate to our initial environment. There are now 1600 deer, but our carrying capacity is 1500. As a result, some of the deer will die of malnutrition, while others will be weakened enough by malnutrition that they become easier prey for predators such as wolves, and a few others might even die fighting over the resources, so the population will quickly drop back below the carrying capacity.
Really simple explanation with graphs with additional info here http://www.dummies.com/how-to/content/the-environmental-science-of-population-growth-mod.html