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What is the equation to find the new population in logistic growth?

1) P(t) = P(0) / (1 + (P(0) / K - 1) * e⁻ʳᵗ)
2) P(t) = P(0) * eʳᵗ / (1 + (P(0) / K - 1) * eʳᵗ)
3) P(t) = P(0) * (1 + (P(0) / K - 1) * e⁻ʳᵗ)
4) P(t) = P(0) / (1 + (P(0) / K - 1) * eʳᵗ)

1 Answer

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Final answer:

The correct equation to find the new population in logistic growth is given by P(t) = P(0) * e^rt / (1 + (P(0) / K - 1) * e^rt), which includes the environmental carrying capacity as a limiting factor.

Step-by-step explanation:

The equation to find the new population in logistic growth among the given options is:

2) P(t) = P(0) * er×t / (1 + (P(0) / K - 1) * er×t)

In logistic growth, the population grows exponentially at first. However, as it approaches the carrying capacity, denoted by K, the growth rate slows down. This is indicated by the term (K - N) in the logistic growth formula, where N is the current population size. If N is close to 0, the population grows nearly exponentially, but as N approaches K, the growth rate declines to zero, displaying an S-shaped curve. The carrying capacity acts as a ceiling that the population cannot exceed due to limiting resources. This equation accommodates for the moderating force that the environment's carrying capacity has on population growth.

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