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

(1,16)
(
1
,
16
)
, (1.5,16.5)
(
1.5
,
16.5
)
, (2,17)
(
2
,
17
)
, (2.5,17.5)
(
2.5
,
17.5
)
, (3,18)
(
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

(15,1)
(
15
,
1
)
, (17.5,1.5)
(
17.5
,
1.5
)
, (20,2)
(
20
,
2
)
, (22.5,2.5)
(
22.5
,
2.5
)
, (25,3)
(
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

Answer 1

To create a function for Ari's charges, we can express it mathematically. The total cost \( C \) based on the number of hours \( h \) can be defined as:

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

Where:
- \( 10 \) is the flat rate.
- \( 15h \) is the charge based on the hours worked.

Now, let's compute how much Ari will make for 1, 1.5, 2, 2.5, and 3 hours using this function.

| Hours (h) | Total Charge (C(h)) |
|-----------|----------------------|
| 1 | \( C(1) = 10 + 15(1) = 10 + 15 = 25 \) |
| 1.5 | \( C(1.5) = 10 + 15(1.5) = 10 + 22.5 = 32.5 \) |
| 2 | \( C(2) = 10 + 15(2) = 10 + 30 = 40 \) |
| 2.5 | \( C(2.5) = 10 + 15(2.5) = 10 + 37.5 = 47.5 \) |
| 3 | \( C(3) = 10 + 15(3) = 10 + 45 = 55 \) |

Now, let's rewrite the data in the format you provided:

1. \( (1, 25) \)
2. \( (1.5, 32.5) \)
3. \( (2, 40) \)
4. \( (2.5, 47.5) \)
5. \( (3, 55) \)

Hence, the responses for the working hours and total charges would look like this:

- \( (1, 25) \)
- \( (1.5, 32.5) \)
- \( (2, 40) \)
- \( (2.5, 47.5) \)
- \( (3, 55) \)

This computes how much Ari makes based on the hours he works.