A skate shop rents roller skates as shown in the table below.
Roller Skate Rentals
| Time | Cost |
| ---------------- | ----- |
| up to 60 minutes | $5 |
| up to 2 hours | $10 |
| up to 5 hours | $20 |
| daily | $25 |
Which graph and function model this situation, where $c$ is the cost, in dollars, of renting skates, and $t$ is the number of hours in a single day that the skates are rented?
$c(t)=\left\{\begin{array}{r}5 \text { if } 0
Answer (2)
Analyze the given roller skate rental costs and the piecewise function.
Compare the costs from the table with the function for each time interval.
Identify discrepancies between the table and the function.
Conclude that the given function does not accurately model the roller skate rental costs. The function is incorrect. F a l se
Explanation
Problem Analysis We are given a table of roller skate rental costs for different time intervals and a piecewise function that models the cost. We need to determine if the given function accurately represents the rental costs in the table.
Given Information The table provides the following information:
Up to 60 minutes (1 hour): $5
Up to 2 hours: $10
Up to 5 hours: $20
Daily: $25
The Piecewise Function The given piecewise function is: c(t)=\left{\begin{array}{r}5 \text { if } 0
The function accurately represents the costs of renting roller skates based on the given table, with correct intervals for pricing. Each pricing tier in the piecewise function aligns with the respective time intervals specified in the table. Therefore, the claim that the function is incorrect is false, as the function is valid.
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