Twenty years ago a small town in texas had a population of 10,000. the population has increased 8% each year since then. what is the growth factor that would be used to solve this problem?

1.08

Step-by-step explanation:

We have been given that 20 ears ago a small town in Texas had a population of 10,000. The population has increased 8% each year since then.

We can see that population is increasing exponentially, so we will use exponential function to write formula for our given information.

, where,

a = Initial value,

b = For growth b is in form (1+r), where r is growth rate in decimal form.

Let us convert our given growth rate in decimal form.

Upon substituting our given values in exponential function formula we will get,

We can see that value of b is 1.08, therefore, growth factor for our given problem is 1.08.

∠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.