Which of the following equations depicts Verhulst-Pearl logistic population growth?
- A.
- B.
- C.
- D.
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Recall the logistic growth model: This model describes population growth that slows down as the population approaches the carrying capacity , unlike exponential growth which has no such limit.
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State the correct equation: The Verhulst-Pearl logistic growth equation is defined as:
Here, is the population size at time , is the intrinsic rate of natural increase, and is the carrying capacity.
- Why this form makes sense: When is small compared to , the term is close to 1, so growth is nearly exponential.
As approaches , the term approaches 0, so growth slows down and eventually stops.
- Eliminate incorrect options: Options A, C, and D use incorrect combinations (such as instead of , or dividing by instead of ), which do not represent this braking effect correctly.
Hence, the answer is Option B.