David wants to rent a bicycle for a couple of hours to explore the city. The price of the bike rental, \[(P)\], depends on the time the bike was out, \[(t)\]. The price consists of a base charge of \[\$8\] and a variable hourly cost. The graph of the function is shown below.

**Complete the following sentences below based on the graph of the function.**

The hourly charge is \[\$\] per hour for the first \[3\] hours.

The rate then drops to \[\$\] per hour until the end of the \[6^{\textrm{th}}\] hour.

The hourly rate drops further to \[\$\] per hour between the \[6^{\textrm{th}}\] and \[10^{\textrm{th}}\] hours.

The maximum price of the bike rental is \[\$\].

To complete the sentences based on the description provided, we can infer the following information:

1. **The hourly charge is** $\$$ **per hour for the first** $3$ **hours.**  
   This charge is typically calculated by finding the slope of the line segment on the graph representing the first three hours.

2. **The rate then drops to** $\$$ **per hour until the end of the** $6^{\textrm{th}}$ **hour.**  
   This charge is calculated by finding the slope of the line segment between the 3rd and 6th hour.

3. **The hourly rate drops further to** $\$$ **per hour between the** $6^{\textrm{th}}$ **and** $10^{\textrm{th}}$ **hours.**  
   This charge is calculated by finding the slope of the line segment between the 6th and 10th hour.

4. **The maximum price of the bike rental is** $\$$.  
   This is typically the total price at the 10th hour, which would be the highest point on the graph.

### To proceed:
- **If you provide the graph or its description in detail**, I can calculate these values accurately.
- Alternatively, if you can provide any specific points on the graph, such as prices at specific hours, that will help me determine the exact amounts for each hourly rate and the maximum price.

Would you like to proceed with any additional details?

Here are 8 related questions:
1. How can you determine the slope of a line segment from a graph?
2. What does the base charge represent in this context?
3. How would the graph change if the hourly rates were higher?
4. What does a decreasing slope represent in the context of this graph?
5. How do you calculate the total price for a specific number of hours from the graph?
6. Can the base charge be adjusted based on time? Why or why not?
7. How can a step-wise function be useful in modeling real-life situations like this one?
8. What are some other real-life scenarios where the pricing changes with time or usage?

**Tip:** To find the slope of a line segment on a graph, use the formula $\text{slope} = \frac{\text{change in } y}{\text{change in } x}$.

Explore how bike rental pricing is determined based on a graph showing hourly charges and base fees. Learn to calculate hourly rates and total rental costs step-by-step. Suitable for students in Grades 7-9.

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