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?

A.2,010 ≤ x ≤ 2,019
B.0 ≤ x ≤ 5,000
C.0 ≤ x ≤ 9
D.All positive integers

Answer 1

Answer:

Option C) $0 \leq x \leq 9$

Step-by-step explanation:

We are given the following information in the question:

The number of users of a cell tower  increased by a factor of 1.5 every year from 2010 to 2019.

$f(x) = 5000(1.5)^x$

where f(x) is the number of cell tower users and x is the years from the year 2010.

We have to find the domain for the given function.

Domain of a function is defined as the possible values of x the function can take, so that the function is defined.

Since this function gives the number of cell users from 2010 to 2019, thus, it is applicable from year 2010 to 2019.

x takes the value of years after 2010.

Thus  for year 2010, x = 0 and for year 2019, x = 9

Thus, the domain of the given function is given by:

$0 \leq x \leq 9$

Answer 2

Answer:

B

Step-by-step explanation:

From the statement, we are given a function that shows the number of cell tower users f(x) after x years, from the year 2010 to 2019, so, to solve the problem, we need to remember that the domain is equal to all the values that the variable (x for this case) could take making the function itself exist.

So, the given function is a function of years, and we know that "x" represents the years from 2010 (starting value), to 2019 (ending value) meaning that the domain is located between those two values.

Hence, the correct option is:

B. 0 ≤ x ≤ 5,000