As the graph shows, the population of Sloths starts off slow, but as time goes on, the population begins to grow. The growth stops as soon as they reach carrying capacity.
The population of sloths started off very small when they immigrated into their habitat, but as time went on they continued making more and more offspring.
As the population increases, the sloths have to compete with each other for the limited resources the habitat has to offer. When there aren't enough resources and food, the habitat reaches carrying capacity. Carrying capacity is how many individuals an environment can support. An example is when all of the trees have been occupied in a sloths habitat, it cannot support any more sloths.
If an environment reaches carrying capacity, and there is not enough space for a family of sloths to live in, they must emigrate out of the habitat and find a place that can support them.
A sloth is a main food source for the jaguar. A sloth is too slow to fight off the fast jaguar. If a jaguar population moves into their habitat, that would cause a decline in population for the sloths. This is also a density-dependent factor, it limits the size of the population.
Another density-dependent factor in a sloths habitat is the amount of food resources they have. Sloths compete with animals like squirrels for their food. If there is not enough food, it can decrease the size of the population.
If a thunderstorm were to take place in the sloth's habitat, causing trees to fall down, it would take away the sloth's home. The sloth would have nowhere to live, therefore it would change the size of the population. This is an example of a density-independent factor.
Another density-independent factor is temperature in the habitat. If it is too hot, they are uncomfortable and can't fall asleep (and they love sleeping). If they are not comfortable in the environment they are living in, they will eventually move into another habitat that comforts them.