\begin{tabular}{|c|c|c|}
\hline \begin{tabular}{l}
Max Visits \\
Per Month
\end{tabular} & \begin{tabular}{c}
Cost Per \\
Visit (\[tex]$)
\end{tabular} & \begin{tabular}{c}
Monthly \\
Fee (\$[/tex])
\end{tabular} \\
\hline 12 & 5 & 15 \\
\hline 16 & 4 & 32 \\
\hline 24 & 3 & 42 \\
\hline
\end{tabular}

Kaleigh wants to know how much she will pay for her gym membership. Which graph represents the total monthly cost at the gym as a function of the number of visits Kaleigh plans to make each month?



Answer :

To find out how much Kaleigh will pay for her gym membership as a function of the number of visits she plans to make each month, we need to calculate the total cost for each given plan based on different numbers of visits. Let's go through each plan step-by-step.

### Plan 1: 12 Visits Maximum
- Cost per visit: [tex]$5 - Monthly fee: $[/tex]15

The total cost for this plan if Kaleigh makes `v` visits in a month will be calculated as:
[tex]\[ \text{Total Cost} = 15 + 5v \][/tex]

For visits from 0 to 24, the costs are:
[tex]\[ \begin{aligned} &0 \text{ visits}: 15 + 5 \times 0 = 15 \\ &1 \text{ visit}: 15 + 5 \times 1 = 20 \\ &2 \text{ visits}: 15 + 5 \times 2 = 25 \\ &\vdots \\ &24 \text{ visits}: 15 + 5 \times 24 = 135 \\ \end{aligned} \][/tex]

The full cost list for visits between 0 to 24 is:
[tex]\[ 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135 \][/tex]

### Plan 2: 16 Visits Maximum
- Cost per visit: [tex]$4 - Monthly fee: $[/tex]32

The total cost for this plan if Kaleigh makes `v` visits in a month will be calculated as:
[tex]\[ \text{Total Cost} = 32 + 4v \][/tex]

For visits from 0 to 24, the costs are:
[tex]\[ \begin{aligned} &0 \text{ visits}: 32 + 4 \times 0 = 32 \\ &1 \text{ visit}: 32 + 4 \times 1 = 36 \\ &2 \text{ visits}: 32 + 4 \times 2 = 40 \\ &\vdots \\ &24 \text{ visits}: 32 + 4 \times 24 = 128 \\ \end{aligned} \][/tex]

The full cost list for visits between 0 to 24 is:
[tex]\[ 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 128 \][/tex]

### Plan 3: 24 Visits Maximum
- Cost per visit: [tex]$3 - Monthly fee: $[/tex]42

The total cost for this plan if Kaleigh makes `v` visits in a month will be calculated as:
[tex]\[ \text{Total Cost} = 42 + 3v \][/tex]

For visits from 0 to 24, the costs are:
[tex]\[ \begin{aligned} &0 \text{ visits}: 42 + 3 \times 0 = 42 \\ &1 \text{ visit}: 42 + 3 \times 1 = 45 \\ &2 \text{ visits}: 42 + 3 \times 2 = 48 \\ &\vdots \\ &24 \text{ visits}: 42 + 3 \times 24 = 114 \\ \end{aligned} \][/tex]

The full cost list for visits between 0 to 24 is:
[tex]\[ 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99, 102, 105, 108, 111, 114 \][/tex]

### Summary
- 12 Visits Max: [tex]\[ 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135 \][/tex]
- 16 Visits Max: [tex]\[ 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 128 \][/tex]
- 24 Visits Max: [tex]\[ 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99, 102, 105, 108, 111, 114 \][/tex]

These results can be used to create graphs that represent the total monthly costs for each plan as a function of the number of visits.