Question

Rosana is tracking how many customers she can serve in a morning. She listed the number of customers served per hour in the following table:

Hour (x) Number of Customers f(x)
1 3
2 5
3 7


Determine if these data represent a linear function or an exponential function, and give the common difference or ratio.
A. This is a linear function because there is a common difference of 2.
B. This is an exponential function because there is a common ratio of 2.
C. This is a linear function because there is a common difference of 3.
D. This is an exponential function because there is a common ratio of 3.

Answer 1

Option: A is the correct answer.

A. This is a linear function because there is a common difference of 2.

Explanation:

Linear function--

A function is said to be linear if the rate of change is constant.

i.e. the function is increasing by a fixed constant.

Here the table is given by:

Hour (x) Number of Customers f(x)

1 3

2 5

3 7

From the table of values we observe that as the value of increasing by 1 the value of y is increasing by 2.

i.e. the rate of change is constant i.e. 2.

Also, the common difference is 2.

since,

5-3=2

and 7-5=2

Hence, the table represents a linear function.

Answer 2

A. This is a linear function because there is a common difference of 2

Explanation:

Differences are ...

• 5 - 3 = 2
• 7 - 5 = 2

The differences of 2 are common, so this is an arithmetic function.