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)

Question

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).