Question

At Robert's Parking Garage, the hourly price depends on how long the car is kept in the lot. Up to the first hour (and for any time less), there's a flat cost of $7.50. After one hour, it costs an additional $3.00 for every additional hour or part of an hour.

Answer 1

The question pertains to the calculation of parking fees at Robert's Parking Garage using a piecewise function which has real-world implications in understanding costs and opportunity costs associated with time and services.

Step-by-step explanation:

At Robert's Parking Garage, the cost structure set up for parking fees is a common mathematical problem that involves understanding piecewise functions and can be explained with a real-life example. Let's say you park your car for an hour and twenty minutes, the cost would be calculated as the flat cost of $7.50 for the first hour plus an additional $3.00 for the additional time. Since the garage charges for any part of an hour, even though you only parked for an additional 20 minutes, you would pay for the full additional hour. The total cost for 1 hour and 20 minutes of parking would be $7.50 + $3.00 which equals $10.50.

Comparably, Aaron's Word Processing Service charges a $31.50 one-time charge plus $32 per hour to determine the total cost. To find the equation that expresses the total cost in terms of the number of hours required to complete the job, we use the expression T(n) = 31.50 + 32n, where n is the number of hours spent on word processing

The concept of opportunity cost is also related to this subject, as exemplified by the airport scenario where the opportunity cost of waiting due to delays is valued at a price, with time being treated as a resource that has a quantifiable financial significance.