A Pet Boarding Service Charges $ 15 \$15 $15 Per Day And An Additional One-time Registration Fee Of $ 25 \$25 $25 . Which Function Represents The Total Cost C ( D C(d C ( D ] For Boarding A Pet For D D D Days?A. C ( D ) = 25 D + 15 C(d) = 25d + 15 C ( D ) = 25 D + 15 B.

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Introduction

Pet boarding services provide a convenient and safe option for pet owners who need to travel or are away from home for an extended period. However, understanding the costs associated with pet boarding is essential to make informed decisions. In this article, we will explore the concept of calculating pet boarding costs using mathematical functions.

Understanding the Problem

A pet boarding service charges a daily rate of $15\$15 and an additional one-time registration fee of $25\$25. The total cost of boarding a pet for dd days can be represented by a mathematical function. Our goal is to determine which function represents the total cost C(d)C(d) for boarding a pet for dd days.

Analyzing the Options

Let's analyze the two options provided:

Option A: C(d)=25d+15C(d) = 25d + 15

This option suggests that the total cost is directly proportional to the number of days the pet is boarded. The coefficient of dd is 2525, which represents the daily rate of $15\$15. However, this option does not account for the one-time registration fee of $25\$25.

Option B: C(d)=25+15dC(d) = 25 + 15d

This option suggests that the total cost is a combination of the one-time registration fee and the daily rate. The constant term 2525 represents the registration fee, while the coefficient of dd is 1515, which represents the daily rate.

Evaluating the Options

To determine which option is correct, let's consider the following scenarios:

  • If the pet is boarded for 1 day, the total cost should be $40\$40 ($25\$25 registration fee + $15\$15 daily rate).
  • If the pet is boarded for 2 days, the total cost should be $50\$50 ($25\$25 registration fee + 2×$152 \times \$15 daily rate).

Let's evaluate the options using these scenarios:

Option A: C(d)=25d+15C(d) = 25d + 15

  • For 1 day: C(1)=25(1)+15=40C(1) = 25(1) + 15 = 40
  • For 2 days: C(2)=25(2)+15=65C(2) = 25(2) + 15 = 65

Option A does not accurately represent the total cost for boarding a pet for 2 days.

Option B: C(d)=25+15dC(d) = 25 + 15d

  • For 1 day: C(1)=25+15(1)=40C(1) = 25 + 15(1) = 40
  • For 2 days: C(2)=25+15(2)=50C(2) = 25 + 15(2) = 50

Option B accurately represents the total cost for boarding a pet for both 1 and 2 days.

Conclusion

Based on our analysis, the correct function that represents the total cost C(d)C(d) for boarding a pet for dd days is:

C(d)=25+15dC(d) = 25 + 15d

This function accurately accounts for the one-time registration fee and the daily rate, providing a comprehensive representation of the total cost.

Real-World Applications

Understanding the concept of calculating pet boarding costs using mathematical functions has practical applications in various industries, such as:

  • Pet care services: Pet boarding services can use this concept to calculate the total cost of boarding a pet for a specific period.
  • Travel planning: Travelers can use this concept to estimate the total cost of pet boarding services while they are away.
  • Financial planning: Individuals can use this concept to budget for pet boarding services and make informed decisions about their financial resources.

Final Thoughts

Introduction

In our previous article, we explored the concept of calculating pet boarding costs using mathematical functions. We analyzed two options and determined that the correct function is C(d)=25+15dC(d) = 25 + 15d. In this article, we will provide a Q&A section to address common questions and concerns related to pet boarding costs.

Q&A

Q: What is the one-time registration fee for pet boarding services?

A: The one-time registration fee for pet boarding services is $25\$25.

Q: How much does it cost to board a pet for 1 day?

A: The cost to board a pet for 1 day is $40\$40 ($25\$25 registration fee + $15\$15 daily rate).

Q: How much does it cost to board a pet for 2 days?

A: The cost to board a pet for 2 days is $50\$50 ($25\$25 registration fee + 2×$152 \times \$15 daily rate).

Q: Can I board my pet for a fraction of a day?

A: Yes, you can board your pet for a fraction of a day. The cost will be calculated based on the number of days your pet is boarded.

Q: How do I calculate the total cost of boarding my pet for a specific period?

A: To calculate the total cost, you can use the function C(d)=25+15dC(d) = 25 + 15d, where dd is the number of days your pet is boarded.

Q: What if I have multiple pets? How do I calculate the total cost?

A: If you have multiple pets, you will need to calculate the total cost for each pet separately and then add them together. For example, if you have two pets and each pet is boarded for 2 days, the total cost would be C(2)+C(2)=50+50=100C(2) + C(2) = 50 + 50 = 100.

Q: Can I negotiate the cost of pet boarding services?

A: It depends on the pet boarding service. Some services may offer discounts or promotions, while others may not. It's best to contact the service directly to inquire about their pricing and policies.

Q: What if I need to board my pet for an extended period? How do I calculate the total cost?

A: If you need to board your pet for an extended period, you can use the function C(d)=25+15dC(d) = 25 + 15d to calculate the total cost. For example, if you need to board your pet for 10 days, the total cost would be C(10)=25+15(10)=175C(10) = 25 + 15(10) = 175.

Real-World Applications

Understanding the concept of calculating pet boarding costs using mathematical functions has practical applications in various industries, such as:

  • Pet care services: Pet boarding services can use this concept to calculate the total cost of boarding a pet for a specific period.
  • Travel planning: Travelers can use this concept to estimate the total cost of pet boarding services while they are away.
  • Financial planning: Individuals can use this concept to budget for pet boarding services and make informed decisions about their financial resources.

Final Thoughts

Calculating pet boarding costs using mathematical functions is a valuable skill that can be applied in various contexts. By understanding the concept of representing total costs using functions, individuals can make informed decisions and plan their finances effectively.

Additional Resources

For more information on calculating pet boarding costs using mathematical functions, you can consult the following resources:

  • Pet care services: Contact local pet boarding services to inquire about their pricing and policies.
  • Mathematical functions: Consult a mathematics textbook or online resource to learn more about mathematical functions and how to apply them in real-world scenarios.
  • Financial planning: Consult a financial advisor or planner to learn more about budgeting and financial planning for pet boarding services.