Question

The charge to rent a trailer is $20 for up to 2 hours plus $8 per additional hour or portion of an hour. Find the cost to rent a trailer for 2.9 hours, 3 hours, and 8.5 hours. Then graph all ordered​ pairs, (hours,​ cost), for the function.

What is the cost to rent a trailer for 2.9 ​hours?

What is the cost to rent a trailer for 3 ​hours?

What is the cost to rent a trailer for 8.5 ​hours?

What is the cost to rent a trailer for 9 hours?

Graph all ordered​ pairs, (hours,​ cost), for the function.

Answer 1

The cost to rent a trailer for 2.9 ​hours is $27.2.

The cost to rent a trailer for 3 ​hours is $28.

The cost to rent a trailer for 8.5 ​hours is $72.

The cost to rent a trailer for 9 ​hours is $76.

Explanation:

It is given that the charge to rent a trailer is $20 for up to 2 hours plus $8 per additional hour or portion of an hour.

Let x be the number of hours.

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

`C(x)=\begin{cases}20 & \text{ if } x\leq 2 \\ 20+8(x-2) & \text{ if } x>2 \end{cases}`

For x>2,

`C(x)=20+8(x-2)`

Substitute x=2.9 in the cost function.

`C(x)=20+8(2.9-2)=27.2`

The cost to rent a trailer for 2.9 ​hours is $27.2.

Substitute x=3 in the cost function.

`C(x)=20+8(3-2)=28`

The cost to rent a trailer for 3 ​hours is $28.

Substitute x=8.5 in the cost function.

`C(x)=20+8(8.5-2)=72`

The cost to rent a trailer for 8.5 ​hours is $72.

Substitute x=9 in the cost function.

`C(x)=20+8(9-2)=76`

The cost to rent a trailer for 9 ​hours is $76.

All ordered​ pairs, in the form of (hours,​ cost) are (2.9, 27.2), (3,28), (8.5, 72) and (9,76).

The graph of all ordered​ pairs is shown below.