Question

A ship carrying 1000 passengers is wrecked on a small island from which the passengers are never rescued. The natural resources of the island restrict the population to a limiting value of 5790​, to which the population gets closer and closer but which it never reaches. The population of the island after time​ t, in​ years, is approximated by the logistic equation given below.

P(t) = 5790/1 + 4.76e^-0.7t
(a) Find the population after 6 years.

Answer 1

5404

Explanation:

P(t) = 5790/(1 + 4.76e^-0.7(6))

= 5404.250311

Answer 2

The population after 6 years is 5404

Explanation:

The population of the island after t years is modeled by the following function:

`P(t) = (5790)/(1 + 4.76e^(-0.76t))`

(a) Find the population after 6 years.

This is P(6).

So

`P(t) = (5790)/(1 + 4.76e^(-0.76t))`

`P(6) = (5790)/(1 + 4.76e^(-0.76*6)) = 5404`

The population after 6 years is 5404