The function is a model for a population A where t is measured in years. The function is a model for a population B where t is measured in years. What is the carrying capacity for the logistic function?
A) 5000
B) 200
C) 3
D) 24
E) 1

Question

The function  is a model for a population A where t is measured in years. The function  is a model for a population B where t is measured in years. What is the carrying capacity for the logistic function?
A) 5000 
B) 200 
C) 3 
D) 24 
E) 1

Quizplus · Accepted Answer

The carrying capacity is represented by the parameter $K$ in the logistic function, which is the maximum population size that can be supported by the environment. In both models, the logistic function is of the form:
$$P(t)=\frac{K}{1+Ae^{-rt}}$$
where $P(t)$ is the population at time $t$, $A$ and $r$ are constants, and $K$ is the carrying capacity. Therefore, to find the carrying capacity, we simply need to identify the value of $K$ in each function. In the first function, the value of $K$ is 5000, which means that the maximum population size that can be supported by the environment is 5000. In the second function, the value of $K$ is 200, which means that the maximum population size that can be supported by the environment is 200. Therefore, the correct answer is A.

The Function Is a Model for a Population a Where