The table in the image shows the rental pricing for different amounts of time at a bicycle rental shop on Cumberland Island, Georgia. You are asked to identify the type of function that models the situation based on the provided data.

The answer choices are:

• a. Step function
• b. Greatest integer function
• c. Absolute value function

Analysis:

• The pricing changes at specific intervals: 1/2 hour, 1 hour, 2 hours, and then a daily rate.
• The price does not vary continuously with time; instead, it jumps from one fixed price to another after a certain period.

This kind of pricing model is best represented by a step function (Option a), where each time interval has a specific charge, and the price increases in steps rather than smoothly or linearly.

The correct answer is a. Step function.

Would you like more details or further explanation?

Related questions:

1. What are the characteristics of a step function in real-world situations?
2. How does a greatest integer function differ from a step function?
3. Could this situation ever be modeled by a linear function? Why or why not?
4. Why would an absolute value function not apply in this situation?
5. What are other examples where step functions are used in pricing models?

Tip:

Step functions are often used in pricing schemes where charges increase at set intervals (like time, weight, or distance).