Question

The number of users of the internet in a town increased by a factor of 1.01 every year from 2000 to 2010. The function below shows the number of internet users f(x) after x years from the year 2000.

f(x) = 3000(1.01)^x

Which of the following is a reasonable domain for the function?

0 ≤ x ≤ 10

2000 ≤ x ≤ 2010

0 ≤ x ≤ 3000

All positive integers

Answer 1

0 ≤ x ≤ 10

Explanation:

Answer 2

0 ≤ x ≤ 10

Explanation

The domain is the possible values that the variable
`x` can take.

The statement "the number of internet users f(x) after x years from the year 2000" is telling us that the x-axis represent the number of years, so the domain of the function is the number of years from 2000 to 2010.

Number of years = 2010 - 2000 = 10 years

So we know that
`x` is at most 10 years; therefore
`x\leq 10`

Since years can't be negative, we can also infer that x must be 0 or bigger than 0, so
`0\leq x`

Now we can combine both inequalities to find the reasonable domain of the function:

`0\leq x\leq 10`