A one-time fee plus a fixed monthly charge signals a linear model: total paid equals the monthly charge times the number of months, plus the fee. Two month-total pairs give the monthly charge by dividing the change in dollars by the change in months; Desmos can handle that arithmetic. The first reported total is not the activation fee unless it was paid at month .
Hints
- Hint 1
The starting value is the amount paid at month . The activation fee is paid once, while the monthly charge is paid times. How would you combine those two parts to write ?
- Hint 2
Each report gives a point written as (months, total dollars). To find the monthly charge, divide the increase in dollars by the number of months that passed. Keep the two changes in the same order.
- Hint 3
Put the -month total into your linear model after finding the monthly charge. The amount left after accounting for four monthly charges is the activation fee, not the entire -month total.
Step-by-step
Find the monthly charge, then the fee
Step 1Write the two parts of the total
Let be the monthly charge and the activation fee. The charge repeats for months, but the fee is paid once, so the linear model is . The monthly charge multiplies the months; the activation fee doesn't.
- Step 2
Pair each month with its total
An ordered pair lists the input first and its matching output second. Here the input is months and the output is dollars paid, so the two reports give and .
- Step 3
Find the charge per month
The rate of change is the increase in dollars divided by the months that passed. Subtract in the same order on top and bottom. Type in Desmos; it shows . So dollars per month.
- Step 4
Find the fee and finish the model
At months, , so put that pair into : . Type in Desmos; tells it to find . Under PARAMETERS, it shows . That's the one-time activation fee, so the total in dollars is . Choice A.