A one-time fee plus a charge each month signals a linear model: total cost equals the starting fee plus the monthly fee times the number of months. Enter both table rows in Desmos and fit a line to find those two fees. One matching row doesn't identify the whole line. Check both rows before choosing an equation.
Hints
- Hint 1
The one-time sign-up fee is the starting value: the cost at zero months. The monthly fee adds the same amount each month, so write , where is the monthly fee and is the sign-up fee.
- Hint 2
Each table row is a point: a month count paired with its total cost. Enter both rows in a Desmos table, with months in the column and cost in the column.
- Hint 3
A regression finds values that make an equation fit the data. Type to find both fees. Which value multiplies the months, and which value is paid once?
Step-by-step
Fit the cost model in Desmos
Step 1Write the two parts of the cost
The constant monthly fee is paid for each month, while the sign-up fee is paid once. So the cost has the form , where is dollars per month and is the fee at .
- Step 2
Enter both cost pairs
The first row pairs 2 months with $110; the second pairs 5 months with $185. Put the month counts in the Desmos table's column and their matching costs in . Both rows matter because one row alone can't determine both fees.
- Step 3
Find the monthly and sign-up fees
Type . The regression fits the table to the cost form from step 1. Desmos shows and under PARAMETERS, so the center charges $25 per month and $60 once at sign-up. The $110 after 2 months includes monthly payments; it isn't the sign-up fee.
- Step 4
Match the equation
Replace and in with the fees you found: . This gives the total cost after months, with the sign-up fee added only once. Choice B.