Question

The number of users of a cell tower in a small, developing town increased by a factor of 1.5 every year from 2010 to 2019. The function below shows the number of cell tower users, f(x), after x years from the year 2010:

f(x) = 5,000(1.5)x

Which of the following is a reasonable domain for the function?
2,010 ≤ x ≤ 2,019
0 ≤ x ≤ 5,000
0 ≤ x ≤ 9
All positive integers
Show work

Answer 1

`2010\leq{x}\leq{2019}`

Explanation:

• The function f(x) shows the number of cell tower users after "x" years from the year 2010.

• Then, the dependent varible of the function f(x) are the number of cell tower users after x years from 2010, and the independent variable of this function, "x", are the years that have passed since 2010, included 2010.

• This means that the independent variable should take the values of the years from 2010, which represent the domain (values that x variable can take), that are all the years between 2010 and 2019 (which is the present year).