A fixed fee plus a charge for each unit signals a linear model: total cost equals a per-unit rate times usage plus a starting fee. Enter both rows in a Desmos table, then use a line regression to find the rate and fee. The first table cost is not necessarily the fixed fee; check whether its usage is zero.
Hints
- Hint 1
A linear model for a fixed fee plus usage has the form . The number is dollars per kWh, while is paid even at zero usage. Which part changes as usage grows?
- Hint 2
In a Desmos table, put usage in and its matching cost in . Enter both rows: one bill alone cannot tell you how much the cost changes per kWh.
- Hint 3
A regression fits a rule to table data. For a straight-line cost rule, type and read and under PARAMETERS. Which value represents the fixed fee?
Step-by-step
Fit the cost rule from the table
Step 1Write the fixed-fee model
The company charges a fee once each month and another amount for every kWh. So use the linear model , where is dollars per kWh and is the fixed fee in dollars. The fixed fee is the cost at zero usage, not necessarily the first cost listed.
- Step 2
Pair each usage with its cost
The rows give and : each pair is a usage and its total cost. Enter a Desmos table with in and in . Desmos shows the two matched bills in the table.
- Step 3
Find the rate and fixed fee
Type . The tilde tells Desmos to fit this linear model to both rows. Under PARAMETERS, it shows and . So usage costs $0.10 per kWh, and the fixed monthly fee is $24.
- Step 4
Give the total-cost equation
Multiply usage by the per-kWh rate, then add the fixed fee once:
This gives the monthly cost in dollars for kWh. Choice D.