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Answer :
Final answer:
The costs to rent a trailer for 2.9 and 3 hours are both $28, for 8.5 and 9 hours are both $76. To plot this function, one must mark these costs against the rental hours, showing a flat rate for the first two hours and additional charges thereafter.
Explanation:
The question asks for the cost of renting a trailer for varying numbers of hours and then requires plotting a graph with these costs against the hours. The rental system has a flat rate of $20 for the first 2 hours, and an additional charge of $8 for each hour or part of an hour thereafter.
- Cost for 2.9 hours: Since any portion of an hour counts as a full hour, renting for 2.9 hours is essentially renting for 3 hours. The first 2 hours cost $20, and for the additional 0.9 (considered as 1) hour, it's $8. Total cost: $20 + $8 = $28.
- Cost for 3 hours: The calculation is the same as for 2.9 hours, so the cost is also $28.
- Cost for 8.5 hours: This includes the first 2 hours plus an additional 6.5 hours (considered as 7 hours). Therefore, the cost is $20 + ($8 x 7) = $20 + $56 = $76.
- Cost for 9 hours: This is calculated similarly, resulting in a cost of $20 + ($8 x 7) = $76.
To graph all ordered pairs, plot points for each of the time periods mentioned with their corresponding costs. Note how the graph demonstrates incremental jumps after the first 2 hours, reflecting the additional $8 charge per hour or part thereof.
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Answer:
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.
Step-by-step 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
[tex]C(x)=\begin{cases}20 & \text{ if } x\leq 2 \\ 20+8(x-2) & \text{ if } x>2 \end{cases}[/tex]
For x>2,
[tex]C(x)=20+8(x-2)[/tex]
Substitute x=2.9 in the cost function.
[tex]C(x)=20+8(2.9-2)=27.2[/tex]
The cost to rent a trailer for 2.9 hours is $27.2.
Substitute x=3 in the cost function.
[tex]C(x)=20+8(3-2)=28[/tex]
The cost to rent a trailer for 3 hours is $28.
Substitute x=8.5 in the cost function.
[tex]C(x)=20+8(8.5-2)=72[/tex]
The cost to rent a trailer for 8.5 hours is $72.
Substitute x=9 in the cost function.
[tex]C(x)=20+8(9-2)=76[/tex]
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.
