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 1, 1.5, 2, 2.5, and 3 hours.

Answer 1

To create a function that represents how much Ari will make based on the number of hours he works, we can define the function \( C(h) \) where \( C \) is the total cost and \( h \) is the number of hours worked.

The formula to calculate the total cost is:

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

Here, the $10 is the flat rate, and \( 15h \) is the additional cost based on the number of hours worked at a rate of $15 per hour.

Now, let's create a table to determine how much Ari will make if he works for 1, 1.5, 2, 2.5, and 3 hours.

| Hours Worked (h) | Total Earnings (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 | \( C(3) = 10 + 15(3) = 10 + 45 = 55 \) |

So the completed table is:

| Hours Worked (h) | Total Earnings (C(h)) |
|-------------------|-----------------------|
| 1 | $25 |
| 1.5 | $32.50 |
| 2 | $40 |
| 2.5 | $47.50 |
| 3 | $55 |

This table shows Ari's earnings based on different hours worked.