A fixed fee plus an hourly charge makes a linear model: each extra hour adds the same amount, while the fixed fee is paid once. Find the hourly rate by dividing the change in cost by the change in hours. Then start from a known total and add the cost of any extra hours. Dividing a total by its hours mistakenly includes the fixed fee in the rate.
Hints
- Hint 1
The hourly rate is the cost added for one more hour. Both rental totals include the same fixed fee, so what happens to that fee when you subtract the totals?
- Hint 2
Start from the 7-hour total instead of finding the fee. In a linear model, each additional hour adds the same amount. How many hours are there from 7 hours to 10 hours?
Step-by-step
Find the hourly rate, then extend the rental
Step 1Find the cost per additional hour
The cost goes from $29 at 3 hours to $53 at 7 hours. The hourly rate is the change in cost divided by the change in hours, so type in Desmos. It shows , or $6 per additional hour. Don't divide $53 by 7: that total includes the fixed fee.
- Step 2
Build the cost rule from 7 hours
Type in Desmos, where is the number of hours and is the total cost in dollars. It stores the rule for the next step. The $53 already includes the fixed fee at 7 hours, so add only the charge for hours beyond 7.
- Step 3
Find the 10-hour cost
Type , which means put 10 hours into the cost rule. Desmos displays , so renting the bike for 10 hours costs $71. Choice B.