A bacteria colony starts with 5 bacteria at the beginning and triples every hour. How would you write an explicit equation to model this situation?

A. f(x) = 3.5*

B. f(x) = 3x + 5

C. f(x) = 5x + 3

D. f(x) = 5.3%

B. f(x) = 3x + 5

Step-by-step explanation:

Initial amount of bacteria N0 = 5 bacteria's

If the triple every hour,

The increase in bacteria in the colony after x hour will be 3*x =3x

x is the amount of hour.

Total amount of bacteria in the colony after x hour will be N0 + 3x

Let f(x) be the total amount of bacteria in the colony after x hour

f(x) = N0+3x

Since N0 = 5

f(x) = 5+3x

Re-arrange

f(x) = 3x + 5

Hence an explicit formula to model the equation is f(x) = 3x + 5

∠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.