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Why does the population size of a species rise and fall around the carrying capacity, rather than immediately stop growing and flatten out once the carrying capacity is reached?

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Competition for resources like food and space cause the growth rate to stop increasing, so the population levels off. ... The carrying capacity (K) is the maximum population size that can be supported in a particular area without destroying the habitat. Limiting factors determine the carrying capacity of a population. Population Growth Limits | CK-12 Foundation
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