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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.

Respuesta :

Answer:

The population after 6 years is 5404

Step-by-step explanation:

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

[tex]P(t) = \frac{5790}{1 + 4.76e^{-0.76t}}[/tex]

(a) Find the population after 6 years.

This is P(6).

So

[tex]P(t) = \frac{5790}{1 + 4.76e^{-0.76t}}[/tex]

[tex]P(6) = \frac{5790}{1 + 4.76e^{-0.76*6}} = 5404[/tex]

The population after 6 years is 5404

amna04352

Answer:

5404

Step-by-step explanation:

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

= 5404.250311

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