Question

A certain area can support 124 deer. Initially, there were 2 deer in the area, and the number has been growing at an average rate of 10% per month. What logistic function describes this situation?

A. P(t) = 124 / (1 + 12e^(-0.1t))
B. P(t) = 2 / (1 + 0.1e^(-12t))
C. P(t) = 2 / (1 + e^(-0.1t))
D. P(t) = 124 / (1 + 0.1e^(12t))

Answer 1

An initial deer population of 2 and a growth rate of 10% per month in an area with a carrying capacity of 124 deer is P(t) = 124 / (1 + 12e^(-0.1t)). The correct answer is option A.

Step-by-step explanation:

The logistic function that accurately describes the growth of a deer population in a given area, where the carrying capacity is 124 deer, the initial population is 2, and the average growth rate is 10% per month, can be represented by a logistic growth equation.

To find the correct logistic function, we must consider both the carrying capacity and the initial population. Option A, P(t) = 124 / (1 + 12e^(-0.1t)), seems to correctly reflect the initial population of 2 deer (since if t=0 then P(t) would be approximately 2), and includes the carrying capacity of 124 deer.

It also accounts for a 10% growth rate per month, indicated by the rate constant of -0.1 in the exponent, which aligns with the provided growth average. Therefore, option A is the most likely choice to describe this logistic function.