Question

The cost, y, of taking a rideshare per hour, x, is shown in the table.

time (hours) 8 9 10 11 12
cost ($)
22.24 25.02 27.80 30.58 33.36
What type of function could be used to model the cost, y, of a rideshare as a function of time, x?

(1 point)
Responses

exponential growth function
exponential growth function

quadratic function
quadratic function

linear function
linear function

exponential decay function
exponential decay function

Answer 1

To determine the type of function that could model the cost of a rideshare as a function of time, we can look at the cost values provided in the table:

- When \( x = 8 \), \( y = 22.24 \)
- When \( x = 9 \), \( y = 25.02 \)
- When \( x = 10 \), \( y = 27.80 \)
- When \( x = 11 \), \( y = 30.58 \)
- When \( x = 12 \), \( y = 33.36 \)

To see if this is a linear function, we can check the differences in cost as the time increases:

- The increase from 8 to 9 hours is \( 25.02 - 22.24 = 2.78 \)
- The increase from 9 to 10 hours is \( 27.80 - 25.02 = 2.78 \)
- The increase from 10 to 11 hours is \( 30.58 - 27.80 = 2.78 \)
- The increase from 11 to 12 hours is \( 33.36 - 30.58 = 2.78 \)

Since the difference in cost remains constant (2.78) as time increases, this indicates a linear relationship.

Therefore, the cost \( y \) of a rideshare as a function of time \( x \) can be modeled by a **linear function**.

So the correct response is:

**linear function**