[Hint: relate this to sigmoid population curve...]
(Describe conditions supporting population growth)
When a population is in an area with abundant resources (like food and den or nesting sites) and low predation, initially there is a large increase in population. Under these conditions the ability of the environment/ecosystem to support the organisms (like rabbits) far exceeds the demands of the initial population. Natality is usually high and, in the absence of a lot of predation or disease causing mortality, the population increases, often exponentially.
(Describe conditions of slowing population growth)
As population increases in an area, the increasing density means: competition for food and habitat, often increasing predator population (supported by a large number of prey) and increase in disease from higher transmission due to crowding. Under these conditions, natality can be reduced by stress and predation as well as fewer resources for food and dens. In addition you may observe emigration as individuals leave the stressful location to look elsewhere for more suitable locations. This reduced natality, increase mortality and increased emigration cause a reduction in population growth.
(Describe conditions of carrying capacity)
The growth of the population slows until, at some point there is a balance between factors reducing population (predation, reduced natality, increased sickness and mortality, emigration) and factors increasing population (immigration, increased natality, immigration). This balance is called the "carrying capacity of the environment." At the carrying capacity, the environment can not support a larger number of individuals.
(other)
In addition to factors directly related to physical needs of organisms, which affects the growth of populations, there are also factors affecting population unrelated to the organsim: density independent factors affecting population. For example, a drought in an area will redue the rainfall and therefore the amount of plant growth and thus the food available to rabbits. The reduced rainfall was not caused by the rabbits or their activities so this is considered a factor independent of the number of rabbits. Similar factors can be natural disasters like floods or earthquakes which significantly alter the environment of the organism.