Question

The charge to rent a trailer is $15 for up to 2 hours plus $8 per additional hour or portion of an hour. Find the cost to rent a trailer for 2.8 hours, 3 hours, and 8.5 hours. Then graph al ordered pairs, (hours, cost), for the function a. What is the cost to rent a trailer for 2.8 hours?

Answer 1

The cost to rent a trailer for 2.8 hours is $21.4.

The cost to rent a trailer for 3 hours is $23.

The cost to rent a trailer for 8.5 hours is $67.

Explanation:

Let x be the number of hours.

It is given that the charge to rent a trailer is $15 for up to 2 hours plus $8 per additional hour or portion of an hour.

The cost to rent a trailer for x hours is defined as

`C(x)=\begin{cases}15 & \text{ if } x\leq 2 \\ 15+8(x-2) & \text{ if } x>2 \end{cases}`

For x>2, the cost function is

`C(x)=15+8(x-2)`

We need to find the cost to rent a trailer for 2.8 hours, 3 hours, and 8.5 hours.

Substitute x=2.8 in the above function.

`C(2.8)=15+8(2.8-2)=15+8(0.8)=21.4`

The cost to rent a trailer for 2.8 hours is $21.4.

Substitute x=3 in the above function.

`C(3)=15+8(3-2)=15+8(1)=23`

The cost to rent a trailer for 3 hours is $23.

Substitute x=8.5 in the above function.

`C(8.5)=15+8(8.5-2)=15+8(6.5)=67`

The cost to rent a trailer for 8.5 hours is $67.

Written all the ordered pairs in the form of (hours, cost).

(2.8,21.4), (3,23) and (8.5,67)

Plot these points on coordinate plane.