Sure, let's break down the problem and find the cost of renting roller skates based on the given time intervals.
Given the rental cost table:
\begin{tabular}{|c|c|}
\hline Time & Cost \\
\hline up to 60 minutes & \$ 5 \\
\hline up to 2 hours & \$ 10 \\
\hline up to 5 hours & \$ 20 \\
\hline daily & \$ 25 \\
\hline
\end{tabular}
First, let's list the time intervals and the corresponding costs:
1. For up to 60 minutes (1 hour), the cost is \$5.
2. For more than 1 hour up to 2 hours, the cost is \$10.
3. For more than 2 hours up to 5 hours, the cost is \$20.
4. For more than 5 hours, the cost is \$25.
Next, let's state the function \( c(t) \) for different \( t \) values, where \( t \) is the time in hours:
1. \( c(t) = 5 \) if \( 0 < t \leq 1 \)
2. \( c(t) = 10 \) if \( 1 < t \leq 2 \)
3. \( c(t) = 20 \) if \( 2 < t \leq 5 \)
4. \( c(t) = 25 \) if \( t > 5 \)
Given this model, we need to determine which graph and function best represent this rental situation:
Graph:
The graph will be a step function that increases at the specified intervals. It will step to \[tex]$5 up to 1 hour, then step to \$[/tex]10 up to 2 hours, then step to \[tex]$20 up to 5 hours, and finally step to \$[/tex]25 for more than 5 hours.
Function:
The piecewise function \( c(t) \) for this rental situation can be represented as:
[tex]\[ c(t) = \begin{cases}
5 & \text{if } 0 < t \leq 1 \\
10 & \text{if } 1 < t \leq 2 \\
20 & \text{if } 2 < t \leq 5 \\
25 & \text{if } t > 5
\end{cases} \][/tex]
Now, apply this model for \( t = 6 \):
- Since \( 6 > 5 \), we refer to the interval for more than 5 hours. According to our function, the cost of renting skates for \( t = 6 \) hours is:
[tex]\[ c(6) = 25 \][/tex]
Thus, the cost of renting skates for 6 hours is \$25.
