Question

The rates for two airport shuttles are shown below: Quick Shuttle Rates for shuttle: $30 for passenger pickup $0.50 for each mile driven Part A: Which shuttle service has a greater initial value? Which service has the greater rate of change? Explain what the greater initial value and greater rate of change mean. Show your work. Part B: Which shuttle company would cost less for a 25-mile trip? Show your work.

Answer 1

The initial value for Quick Shuttle is $30, and the rate of change is $0.50 per mile. For a 25-mile trip, Quick Shuttle's total cost is $42.50.

Step-by-step explanation:

The initial value for Quick Shuttle is $30, which is the passenger pickup fee. The rate of change is $0.50 per mile, which is the cost for each mile driven. The initial value represents the fixed cost for getting the service, while the rate of change represents the variable cost per unit of distance traveled.

Without information on the second shuttle's rates, we'll only compare the cost for Quick Shuttle for a 25-mile trip. The cost can be calculated by the initial value plus the product of the rate of change and the distance:

Total cost for Quick Shuttle = Initial value + (Rate of change × Miles driven)

Total cost for Quick Shuttle = $30 + ($0.50 × 25 miles) = $30 + $12.50 = $42.50.

Thus, for a 25-mile trip, Quick Shuttle would cost $42.50.

Answer 2

- Part A: The shuttle service with the greater initial value is Quick Shuttle, as it charges $30 for passenger pickup compared to the other service. The service with the greater rate of change is also Quick Shuttle, as it charges $0.50 for each mile driven.

- Part B: Quick Shuttle would cost less for a 25-mile trip, given its initial value and rate of change.

Step-by-step explanation:

Part A:

The greater initial value refers to the starting cost of the service. In this case, Quick Shuttle has a $30 initial value for passenger pickup, while the other service does not have a specific initial pickup cost mentioned. The greater rate of change refers to the cost incurred per unit, and Quick Shuttle charges $0.50 for each mile driven, which is higher than the other service. This means Quick Shuttle starts with a higher base cost and increases the fare more rapidly per mile.

Part B:

To determine the cost for a 25-mile trip, we calculate the total cost for each shuttle service. For Quick Shuttle, the cost would be $30 (initial value) + $0.50/mile * 25 miles. For the other service, it would depend on the rate per mile. Since the rate is not provided, we cannot provide an exact cost. Therefore, Quick Shuttle would cost less for a 25-mile trip based on the given information.

In summary, the greater initial value means a higher starting cost, and the greater rate of change indicates a steeper increase in cost per unit. Quick Shuttle outperforms the other service in both aspects.