Question

The natural resources of an island limit the growth of the population. The population of the island is given by the logistic equation where t is the number of years after 1980. What is the limiting value of the population?

Answer 1

The correct option is (a) 3759.

Explanation:

The complete question is:

The natural resources of an island limit the growth of the population. The population of the island is given by the logistic equation
`P(t)=(3759)/(1+3.94e^(-0.38t))`where t is the number of years after 1980. What is the limiting value of the population?

(a) 3759

(b) 23

(c) 761

(d) 1017

Solution:

The limiting value is the value of the function P (t) for t → ∞.

As t → ∞, the expression
`(3.94e^(-0.38t))` → 0.

Thus, making the denominator of P (t) 1.

So, the limiting value of the population is, 3759.

Thus, the correct option is (a) 3759.