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

(1,5), (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

(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.

Answer 1

To create a function that determines how much Ari makes based on the number of hours he works, we can define the function as follows:

Let \( x \) be the number of hours worked. The total amount Ari makes, \( f(x) \), can be expressed as:

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

Now, we will calculate \( f(x) \) for the specified values of \( x \): 1, 1.5, 2, 2.5, and 3 hours.

1. For \( x = 1 \):
\[
f(1) = 10 + 15(1) = 10 + 15 = 25
\]

2. For \( x = 1.5 \):
\[
f(1.5) = 10 + 15(1.5) = 10 + 22.5 = 32.5
\]

3. For \( x = 2 \):
\[
f(2) = 10 + 15(2) = 10 + 30 = 40
\]

4. For \( x = 2.5 \):
\[
f(2.5) = 10 + 15(2.5) = 10 + 37.5 = 47.5
\]

5. For \( x = 3 \):
\[
f(3) = 10 + 15(3) = 10 + 45 = 55
\]

Now let's organize this information into a table:

\[
\begin{array}{|c|c|}
\hline
\text{Hours Worked (x)} & \text{Total Earnings (f(x))} \\
\hline
1 & 25 \\
1.5 & 32.5 \\
2 & 40 \\
2.5 & 47.5 \\
3 & 55 \\
\hline
\end{array}
\]

Based on these calculations, the correct response from the options given is:

**(1, 25), (1.5, 32.5), (2, 40), (2.5, 47.5), (3, 55)**.