A customer paid a one-time sign-up fee of $25 and then $40 each month for a streaming service. The equation above represents the total amount, in dollars, the customer has paid after months. How many months has the customer had the streaming service?
A one-time fee plus a charge "each month" signals a linear cost equation: the fixed fee plus the monthly charge times the number of months equals the total. Read what the variable counts, then use a one-unknown Desmos regression to solve the given equation. The fixed fee is paid once, so don't multiply it by the month count.
Hints
- Hint 1
A constant term stays the same as the number of months changes. The sign-up fee is paid only once. Which part of the equation represents the charge that grows with each month?
- Hint 2
The variable counts months, while counts dollars paid for those months. To solve in Desmos, use in place of and in place of .
Step-by-step
Interpret the charges, then solve in Desmos
Step 1Identify what repeats
The one-time $25 fee is charged once, while is $40 for each of months. So counts months, not dollars. Only the per-month charge gets multiplied by the number of months.
- Step 2
Find the number of months
Type in Desmos. Use instead of so Desmos solves for a value rather than making a slider; tells it to fit the equation. Under PARAMETERS, Desmos shows . Since counts months, the customer has had the service for 6 months. Choice B.