Population growth refers to the change in the number of individuals of a species in an ecosystem over time. A population may increase when individuals are born or enter an area, and it may decrease when individuals die or leave the area. Carrying capacity is the maximum population size that an ecosystem can support for a long period of time based on the resources and conditions available. These concepts help us understand why populations do not continue increasing indefinitely. For example, a pond can support only a certain number of fish because it has a limited amount of food, oxygen, space, and shelter. The carrying capacity of an ecosystem can change when environmental conditions change. 

Under ideal conditions, a population can increase rapidly because organisms have abundant resources and favorable environmental conditions. There is sufficient food, water, space, shelter, and mates, while factors such as disease, predation, and competition are minimal. When individuals reproduce successfully, the population becomes larger, allowing more organisms to reproduce. This can result in exponential growth, in which the population increases at an increasingly rapid rate. For example, if bacteria have enough nutrients, moisture, and suitable temperature, their numbers can increase very quickly. 

As a population becomes larger, its organisms require more resources to survive. When food, water, space, shelter, or other resources become limited, organisms must compete with one another for what is available. This competition can reduce access to resources, resulting in slower reproduction, reduced survival, or increased mortality. Therefore, the rate of population growth decreases as resource limitations become stronger. For example, if too many fish live in a small pond, available food and oxygen may become insufficient, causing the population's growth to slow. 

Population-growth graphs allow us to observe and interpret changes in population size over time. In a typical logistic growth graph, the population initially increases rapidly. As the population becomes larger, growth begins to slow because resources and other environmental factors increasingly limit further growth. Eventually, the graph levels off around the carrying capacity, represented by the maximum population size the environment can sustainably support. Students should be able to identify the rapid-growth phase, slowing-growth phase, and carrying-capacity level from a graph. 

In real ecosystems, populations are affected by changing environmental conditions and multiple factors at the same time. Students can use what they learned to predict what will happen when a population approaches, reaches, or exceeds its carrying capacity. For example, if a deer population increases in a forest, food may eventually become scarce. Competition may increase, reproduction may decrease, and deaths may increase, causing the population to stop increasing or decline. If additional food or habitat becomes available, the ecosystem's carrying capacity may increase. Thus, population size can fluctuate around carrying capacity rather than remaining permanently constant.