Representing Functions Quick Check

Question

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Question
Ari is starting a yard service business. He charges a flat rate of $10 plus an additional $15 per hour, regardless of the service. Create a function and use a table to determine how much Ari will make if he works for 1, 1.5, 2, 2.5, and 3 hours.(1 point)
Responses

(1,25), (1.5,32.5), (2,40), (2.5,47.5), (3,55)
left parenthesis 1 comma 25 right parenthesis , left parenthesis 1.5 comma 32.5 right parenthesis , left parenthesis 2 comma 40 right parenthesis , left parenthesis 2.5 comma 47.5 right parenthesis , left parenthesis 3 comma 55 right parenthesis

(15,1), (17.5,1.5), (20,2), (22.5,2.5), (25,3)
left parenthesis 15 comma 1 right parenthesis , left parenthesis 17.5 comma 1.5 right parenthesis , left parenthesis 20 comma 2 right parenthesis , left parenthesis 22.5 comma 2.5 right parenthesis , left parenthesis 25 comma 3 right parenthesis

(1,5), (1.5,7.5), (2,10), (2.5,12.5), (3,15)
left parenthesis 1 comma 5 right parenthesis , left parenthesis 1.5 comma 7.5 right parenthesis , left parenthesis 2 comma 10 right parenthesis , left parenthesis 2.5 comma 12.5 right parenthesis , left parenthesis 3 comma 15 right parenthesis

(1,16), (1.5,16.5), (2,17), (2.5,17.5), (3,18)
left parenthesis 1 comma 16 right parenthesis , left parenthesis 1.5 comma 16.5 right parenthesis , left parenthesis 2 comma 17 right parenthesis , left parenthesis 2.5 comma 17.5 right parenthesis , left parenthesis 3 comma 18 right parenthesis
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Answer 1

To determine how much Ari will make based on the hours he works, we can create a function that represents his earnings. The function can be expressed as:

\[ E(h) = 10 + 15h \]

where \( E(h) \) is the earnings for \( h \) hours worked, the $10 is the flat rate, and each hour worked adds $15.

Now let's calculate the earnings for the specified hours (1, 1.5, 2, 2.5, and 3):

1. For \( h = 1 \): \[ E(1) = 10 + 15(1) = 10 + 15 = 25 \]

2. For \( h = 1.5 \): \[ E(1.5) = 10 + 15(1.5) = 10 + 22.5 = 32.5 \]

3. For \( h = 2 \): \[ E(2) = 10 + 15(2) = 10 + 30 = 40 \]

4. For \( h = 2.5 \): \[ E(2.5) = 10 + 15(2.5) = 10 + 37.5 = 47.5 \]

5. For \( h = 3 \): \[ E(3) = 10 + 15(3) = 10 + 45 = 55 \]

Now we can summarize the results in a table:

| Hours Worked (h) | Earnings (E(h)) | |-------------------|------------------| | 1 | 25 | | 1.5 | 32.5 | | 2 | 40 | | 2.5 | 47.5 | | 3 | 55 |

Thus, the correct response matches the first option: (1, 25), (1.5, 32.5), (2, 40), (2.5, 47.5), (3, 55).