Answer:
The correct option is (a) 3759.
Step-by-step 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 [tex]P(t)=\frac{3759}{1+3.94e^{-0.38t}}[/tex]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 [tex](3.94e^{-0.38t})[/tex] → 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.
