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

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).

Answer 2

0 ≤ x ≤ 9

Explanation:

Mathematically speaking, the domain is all positive integers given that potential function is continous. Nonetheless, this model was considered by taking information from 2010 to 2019 into account and there is risk that output may be unreliable for x > 9. Hence, a reasonable domain for the function is 0 ≤ x ≤ 9