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.

Answer 1

To determine how much Ari will make based on the hours he works, we can create a function and then use a table to outline the earnings for specific hours worked.

### Function
Let \( E(h) \) be the total earnings Ari makes for working \( h \) hours. The flat rate is $10, and he charges $15 per hour. The function can be expressed as:

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

### Table of Earnings
Now, we'll calculate \( E(h) \) for \( h = 1, 1.5, 2, 2.5, \) and \( 3 \).

| Hours Worked (h) | Earnings, \( E(h) \) |
|-------------------|----------------------|
| 1 | \( E(1) = 10 + 15(1) = 10 + 15 = 25 \) |
| 1.5 | \( E(1.5) = 10 + 15(1.5) = 10 + 22.5 = 32.5 \) |
| 2 | \( E(2) = 10 + 15(2) = 10 + 30 = 40 \) |
| 2.5 | \( E(2.5) = 10 + 15(2.5) = 10 + 37.5 = 47.5 \) |
| 3 | \( E(3) = 10 + 15(3) = 10 + 45 = 55 \) |

### Summary of Earnings
- For 1 hour: $25
- For 1.5 hours: $32.50
- For 2 hours: $40
- For 2.5 hours: $47.50
- For 3 hours: $55

This table shows how much Ari will earn based on the hours he works.