In a logistic growth model, the curve levels off at a point called the carrying capacity (K), where the growth rate becomes zero (dN/dt = 0). When a population grows in an environment with limited resources, it follows this logistic growth pattern, represented by the equation dN/dt = rN[(K

Question

In a logistic growth model, the curve levels off at a point called the carrying capacity (K), where the growth rate becomes zero (dN/dt = 0). When a population grows in an environment with limited resources, it follows this logistic growth pattern, represented by the equation dN/dt = rN[(K-N)/K]. If K equals N, then the term (K-N)/K becomes zero. Is this statement correct?

Accepted Answer

True. In the logistic equation, the factor $(K-N)/K$ measures how much room is left for growth. If $N = K$, that factor becomes $0$, so $dN/dt = 0$ and the population stops increasing.

Solution

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