A Hotel Offers A Reward Program Based On The Number Of Nights Stayed. The Function F ( X F(x F ( X ] Represents The Number Of Free Nights Earned As A Function Of X X X , The Number Of Nights Stayed.$[ F(x)=\left\lfloor\frac{x}{10}\right\rfloor

by ADMIN 244 views

Introduction

In the hospitality industry, hotel reward programs have become a popular way to incentivize customers to stay with a particular hotel chain. These programs often offer rewards based on the number of nights stayed, with the goal of encouraging loyalty and repeat business. In this article, we will explore a hotel reward program that offers a reward based on the number of nights stayed, and examine the math behind the free nights earned.

The Reward Program

The hotel reward program in question offers a reward based on the number of nights stayed, with the reward being calculated using the function f(x)=⌊x10⌋f(x)=\left\lfloor\frac{x}{10}\right\rfloor, where xx represents the number of nights stayed and f(x)f(x) represents the number of free nights earned. This function is a simple example of a mathematical concept known as the floor function, which rounds a number down to the nearest integer.

Understanding the Floor Function

The floor function, denoted by ⌊x⌋\lfloor x \rfloor, is a mathematical function that takes a real number xx as input and returns the largest integer less than or equal to xx. In other words, it rounds xx down to the nearest integer. For example, ⌊3.7⌋=3\lfloor 3.7 \rfloor = 3, ⌊5⌋=5\lfloor 5 \rfloor = 5, and ⌊−2.3⌋=−3\lfloor -2.3 \rfloor = -3.

Applying the Floor Function to the Reward Program

In the context of the hotel reward program, the floor function is used to calculate the number of free nights earned based on the number of nights stayed. For example, if a customer stays for 17 nights, the number of free nights earned would be ⌊1710⌋=1\lfloor \frac{17}{10} \rfloor = 1. Similarly, if a customer stays for 25 nights, the number of free nights earned would be ⌊2510⌋=2\lfloor \frac{25}{10} \rfloor = 2.

Calculating Free Nights Earned

To calculate the number of free nights earned, we can use the floor function to divide the number of nights stayed by 10. The result will be the number of free nights earned. For example:

  • If a customer stays for 7 nights, the number of free nights earned would be ⌊710⌋=0\lfloor \frac{7}{10} \rfloor = 0.
  • If a customer stays for 12 nights, the number of free nights earned would be ⌊1210⌋=1\lfloor \frac{12}{10} \rfloor = 1.
  • If a customer stays for 27 nights, the number of free nights earned would be ⌊2710⌋=2\lfloor \frac{27}{10} \rfloor = 2.

Graphing the Reward Program

To visualize the reward program, we can graph the function f(x)=⌊x10⌋f(x)=\left\lfloor\frac{x}{10}\right\rfloor. The graph will show the number of free nights earned based on the number of nights stayed.

Graph

import matplotlib.pyplot as plt
import numpy as np

x = np.arange(0, 100, 1)
y = np.floor(x/10)


plt.plot(x, y)
plt.xlabel('Number of Nights Stayed')
plt.ylabel('Number of Free Nights Earned')
plt.title('Hotel Reward Program')
plt.grid(True)
plt.show()

Conclusion

In conclusion, the hotel reward program offers a reward based on the number of nights stayed, with the reward being calculated using the floor function. The floor function rounds a number down to the nearest integer, making it a simple and effective way to calculate the number of free nights earned. By understanding the math behind the reward program, customers can make informed decisions about their loyalty and repeat business.

Frequently Asked Questions

  • Q: How does the reward program work? A: The reward program offers a reward based on the number of nights stayed, with the reward being calculated using the floor function.
  • Q: What is the floor function? A: The floor function is a mathematical function that takes a real number as input and returns the largest integer less than or equal to the input.
  • Q: How do I calculate the number of free nights earned? A: To calculate the number of free nights earned, you can use the floor function to divide the number of nights stayed by 10.

References

Introduction

In our previous article, we explored a hotel reward program that offers a reward based on the number of nights stayed, with the reward being calculated using the floor function. In this article, we will answer some frequently asked questions about the reward program and provide additional information to help customers understand how it works.

Q&A

Q: How does the reward program work?

A: The reward program offers a reward based on the number of nights stayed, with the reward being calculated using the floor function. The floor function rounds a number down to the nearest integer, making it a simple and effective way to calculate the number of free nights earned.

Q: What is the floor function?

A: The floor function is a mathematical function that takes a real number as input and returns the largest integer less than or equal to the input. For example, ⌊3.7⌋=3\lfloor 3.7 \rfloor = 3, ⌊5⌋=5\lfloor 5 \rfloor = 5, and ⌊−2.3⌋=−3\lfloor -2.3 \rfloor = -3.

Q: How do I calculate the number of free nights earned?

A: To calculate the number of free nights earned, you can use the floor function to divide the number of nights stayed by 10. For example, if you stay for 17 nights, the number of free nights earned would be ⌊1710⌋=1\lfloor \frac{17}{10} \rfloor = 1.

Q: What is the benefit of using the floor function in the reward program?

A: The floor function is a simple and effective way to calculate the number of free nights earned. It ensures that the reward is always an integer, making it easy to understand and calculate.

Q: Can I earn free nights if I stay for a fraction of a night?

A: No, the reward program only rewards customers for whole nights stayed. If you stay for a fraction of a night, you will not earn any free nights.

Q: How do I track my free nights earned?

A: You can track your free nights earned by keeping a record of the number of nights you stay and using the floor function to calculate the number of free nights earned.

Q: Can I use my free nights earned at any hotel?

A: Yes, you can use your free nights earned at any hotel that participates in the reward program.

Q: How do I redeem my free nights earned?

A: To redeem your free nights earned, you can contact the hotel directly and provide your loyalty number. The hotel will then apply the free nights earned to your account.

Q: Can I earn free nights if I stay at multiple hotels?

A: Yes, you can earn free nights at multiple hotels that participate in the reward program. However, you will only earn free nights for the number of nights stayed at each individual hotel.

Q: How do I know if a hotel participates in the reward program?

A: You can check the hotel's website or contact them directly to see if they participate in the reward program.

Conclusion

In conclusion, the hotel reward program offers a simple and effective way to earn free nights based on the number of nights stayed. By understanding how the reward program works and using the floor function to calculate the number of free nights earned, customers can make informed decisions about their loyalty and repeat business.

Frequently Asked Questions (FAQs)

  • Q: How does the reward program work? A: The reward program offers a reward based on the number of nights stayed, with the reward being calculated using the floor function.
  • Q: What is the floor function? A: The floor function is a mathematical function that takes a real number as input and returns the largest integer less than or equal to the input.
  • Q: How do I calculate the number of free nights earned? A: To calculate the number of free nights earned, you can use the floor function to divide the number of nights stayed by 10.

References