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 create a function that represents how much Ari makes based on the number of hours he works, we can define a function \( f(h) \) where \( h \) is the number of hours worked.

The total charge Ari makes is composed of a flat rate of $10 plus an additional $15 per hour. Thus, the function can be expressed as:

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

Now, we can use this function to create a table showing how much Ari will make if he works for 1, 1.5, 2, 2.5, and 3 hours.

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

### Summary of Total 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 clearly shows how much Ari will make depending on the number of hours he works.