To determine the reasonable range for the function representing the cost of renting a car from a company that charges $10 per hour (with any part of an hour rounding up to the next full hour), and has a limit of 8 hours, we can analyze the pricing structure.
-
Cost Calculation:
- If you rent the car for \( h \) hours, the cost \( C \) can be calculated as follows: \[ C = 10 \cdot \lceil h \rceil \] where \( \lceil h \rceil \) is the ceiling function that rounds \( h \) up to the next full hour.
-
Possible Values for Hours Rented:
- Since the company has a limit of 8 hours, \( h \) can take any value from 1 hour up to 8 hours, including fractional hours.
- Therefore, \( h \) can range from 0 (although in practice, you would pay for a minimum of 1 hour) to 8.
-
Cost Calculation for Each Case:
- For \( h = 1 \): \( C = 10 \cdot \lceil 1 \rceil = 10 \) dollars
- For \( h = 2 \): \( C = 10 \cdot \lceil 2 \rceil = 20 \) dollars
- For \( h = 3 \): \( C = 10 \cdot \lceil 3 \rceil = 30 \) dollars
- For \( h = 4 \): \( C = 10 \cdot \lceil 4 \rceil = 40 \) dollars
- For \( h = 5 \): \( C = 10 \cdot \lceil 5 \rceil = 50 \) dollars
- For \( h = 6 \): \( C = 10 \cdot \lceil 6 \rceil = 60 \) dollars
- For \( h = 7 \): \( C = 10 \cdot \lceil 7 \rceil = 70 \) dollars
- For \( h = 8 \): \( C = 10 \cdot \lceil 8 \rceil = 80 \) dollars
-
Range of Costs:
- Based on the calculations above, the cost can be \( 10, 20, 30, 40, 50, 60, 70, \) or \( 80 \) dollars, depending on how many full hours (including any parts of an hour rounded up) the car is rented for.
- Therefore, the reasonable range for the function, which indicates total costs, is: \[ \text{Range} = {10, 20, 30, 40, 50, 60, 70, 80} \]
Thus, the reasonable range of the cost function, given the company's pricing policy, is the set of amounts above.