A price that covers an initial block of time, then adds the same charge for each extra hour, calls for a linear model built from the end of that block. Subtract the covered hours from the total before applying the hourly rate, then add the initial price once. Applying the rate to every hour charges for hours already covered.
Hints
- Hint 1
Think of as the total number of hours. The first have already been paid for, so take them away before applying the extra-hour rate. How many hours are left?
- Hint 2
An hourly rate multiplies only the hours it applies to. Multiply the extra hours by $4.25, then add the one-time $9.50 charge rather than multiplying that charge by .
Step-by-step
Build from the two-hour charge
Step 1Count the additional hours
No Desmos needed. The charges turn directly into a function. The first hours are covered by the initial price, so a rental lasting hours has additional hours. Count only the hours past the paid-for block.
- Step 2
Find the additional charge
Each additional hour costs $4.25, so the additional charge is dollars. Multiplying by instead would charge for the first two hours again.
- Step 3
Add the initial charge
The $9.50 pays for the first two hours once, so add it to the additional charge: . This gives the total cost, in dollars, for hours. Choice C.