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.
### 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.
