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

(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

(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

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

Answer 1

To create a function that represents the total earnings of Ari's yard service business, we can combine the flat rate and the hourly rate. The function can be defined as:

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

where \( E(h) \) is the total earnings after \( h \) hours of work, and the flat rate is $10 with an additional $15 per hour.

Now, let's calculate Ari's earnings for 1, 1.5, 2, 2.5, and 3 hours:

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

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

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

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

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

Now, we can summarize this information 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 from the options given is:
**(1, 25), (1.5, 32.5), (2, 40), (2.5, 47.5), (3, 55)**.