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To solve a problem involving the greatest integer function, it is important to understand the function well. It is also important to learn how to solve the equation algebraically for a problem without context. For more details, see the following concept sheet: Solving a Step Function Equation.
Justin needs a lawyer to settle a dispute with his landlord regarding certain clauses in his lease. He contacts a lawyer specializing in property leases. The lawyer's fees are the following: for each partial or full period of |15| minutes, the lawyer charges |\$ 45|. Fortunately, taxes are included.
a) If studying the case requires |3| hours and |24| minutes, how much will it cost Justin?
b) When the case is completely settled, Justin calculates that he paid a total of |\$ 2\ 700| in fees. For how many hours did the lawyer bill him for?
Dominik rents movies from his favorite video store once a week. Unfortunately, he has the annoying habit of not returning his films on time. A movie costs |\$ 2.50| on the first day. The film must be returned after one day or else he must pay a late fee of |\$ 3.00| per day.
a) Determine the equation of the function modeling this situation and draw the graph.
b) How much does Dominik have to pay if he brings back his film |6| days later?