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.