Certainly! Let's analyze the gym membership plans step by step to determine the total cost for different numbers of visits Kaleigh might make each month. We'll break down the cost calculation for various ranges according to the membership plan:
### Membership Plan Breakdown:
1. Plan 1:
- Maximum Visits: 12
- Cost Per Visit: [tex]$5
- Monthly Fee: $[/tex]15
2. Plan 2:
- Maximum Visits: 16
- Cost Per Visit: [tex]$4
- Monthly Fee: $[/tex]32
3. Plan 3:
- Maximum Visits: 24
- Cost Per Visit: [tex]$3
- Monthly Fee: $[/tex]42
### Calculating Total Monthly Cost:
We'll calculate the total monthly cost for different visit counts, ensuring the costs align with each plan's conditions.
1. 0 visits:
- Follows Plan 1: Total Cost = 0 * [tex]$5 + $[/tex]15 = [tex]$15
2. 5 visits:
- Follows Plan 1: Total Cost = 5 $[/tex]5 + [tex]$15 = $[/tex]25 + [tex]$15 = $[/tex]40
3. 12 visits:
- Follows Plan 1: Total Cost = 12 [tex]$5 + $[/tex]15 = [tex]$60 + $[/tex]15 = [tex]$75
4. 15 visits:
- Beyond Plan 1 but within Plan 2: Total Cost = 15 $[/tex]4 + [tex]$32 = $[/tex]60 + [tex]$32 = $[/tex]92
5. 16 visits:
- Follows Plan 2: Total Cost = 16 [tex]$4 + $[/tex]32 = [tex]$64 + $[/tex]32 = [tex]$96
6. 20 visits:
- Beyond Plan 2 but within Plan 3: Total Cost = 20 $[/tex]3 + [tex]$42 = $[/tex]60 + [tex]$42 = $[/tex]102
7. 24 visits:
- Follows Plan 3: Total Cost = 24 [tex]$3 + $[/tex]42 = [tex]$72 + $[/tex]42 = [tex]$114
### Summarized Results:
Below are the total costs for the given visits:
- 0 visits: $[/tex]15
- 5 visits: [tex]$40
- 12 visits: $[/tex]75
- 15 visits: [tex]$92
- 16 visits: $[/tex]96
- 20 visits: [tex]$102
- 24 visits: $[/tex]114
From the above calculations, a graph representing the total monthly cost as a function of the visits Kaleigh plans to make each month should accurately reflect these cost points. The y-axis would represent the cost, and the x-axis would represent the number of visits per month. The graph would show distinct linear segments with breakpoints at 12, 16, and 24 visits, reflecting transitions between different plans.
