A conservation organization releases 50 foxes into a preserve. After 5 years, there are 85 foxes in the preserve. The preserve has a carrying capacity of 225. Determine the population after 10 years. Discard any fractional part of your answer.
A)126
B)118
C)139
D)131
E)205

Question

Quizplus · Accepted Answer

The population growth can be modeled by the logistic growth equation, which accounts for the carrying capacity. The formula for logistic growth is P(t) = K / (1 + ((K - P0)/P0) * e^(-rt)), where P(t) is the population at time t, K is the carrying capacity, P0 is the initial population, r is the growth rate, and e is the base of the natural logarithm. Without the exact growth rate (r), we can't directly apply this formula. However, we can estimate the growth using the given information and the concept that the growth rate decreases as the population approaches the carrying capacity. Given the initial increase from 50 to 85 over 5 years, we can infer a slowing growth rate that won't reach the carrying capacity within the next 5 years. Among the provided options, 126 is a reasonable estimate for a growing population that hasn't reached its carrying capacity, considering the slowing growth rate as the population size increases.

A Conservation Organization Releases 50 Foxes into a Preserve