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.

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:

(a) Find the population after 6 years.

This is P(6).

So

The population after 6 years is 5404

5404

Step-by-step explanation:

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

= 5404.250311

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

take it another