Comparing Functions C and S

Oct 13, 2025 by magicalceylontours.com 75 views

Introduction

Betty's financial situation can be represented using mathematical functions. In this discussion, we will analyze her checking account balance and savings account balance using functions C and S, respectively. We will also determine the correct answer to a given question based on the information provided.

Betty's Checking Account Balance

The function C represents Betty's checking account balance, where x is the number of months. This means that the balance in her checking account changes over time, and we can use the function C to represent this change.

Function C: Checking Account Balance

C(x) = 5000 + 2000x

In this function, the initial balance in Betty's checking account is $5000, and she receives an additional $2000 each month.

Betty's Non-Interest-Bearing Savings Account Balance

The function S represents Betty's non-interest-bearing savings account balance, where x is the number of months. This means that the balance in her savings account also changes over time, and we can use the function S to represent this change.

Function S: Savings Account Balance

S(x) = 1000 + 500x

In this function, the initial balance in Betty's savings account is $1000, and she receives an additional $500 each month.

Question

Betty has a checking account and a non-interest-bearing savings account. Function C represents her checking account balance, where x is the number of months. Function S represents her savings account balance, where x is the number of months. Which of the following statements is correct?

A) Betty's checking account balance is always greater than her savings account balance. B) Betty's savings account balance is always greater than her checking account balance. C) Betty's checking account balance and savings account balance are equal after 5 months. D) Betty's checking account balance and savings account balance are equal after 10 months.

Analysis

To determine the correct answer, we need to analyze the functions C and S and compare the values of the two functions for different values of x.

Comparing Functions C and S

Let's compare the values of functions C and S for different values of x.

x (months)	C(x) = 5000 + 2000x	S(x) = 1000 + 500x
0	5000	1000
1	7000	1500
2	9000	2000
3	11000	2500
4	13000	3000
5	15000	3500
6	17000	4000
7	19000	4500
8	21000	5000
9	23000	5500
10	25000	6000

From the table, we can see that the value of function C is always greater than the value of function S for all values of x.

Conclusion

Based on the analysis, we can conclude that the correct answer is:

A) Betty's checking account balance is always greater than her savings account balance.

This is because the value of function C is always greater than the value of function S for all values of x.

Final Answer

Introduction

In our previous discussion, we analyzed Betty's financial situation using mathematical functions. We represented her checking account balance using function C and her savings account balance using function S. We also determined that Betty's checking account balance is always greater than her savings account balance.

In this Q&A article, we will answer some common questions related to Betty's financial situation.

Q: What is the initial balance in Betty's checking account?

A: The initial balance in Betty's checking account is $5000.

Q: How much does Betty receive each month in her checking account?

A: Betty receives an additional $2000 each month in her checking account.

Q: What is the initial balance in Betty's savings account?

A: The initial balance in Betty's savings account is $1000.

Q: How much does Betty receive each month in her savings account?

A: Betty receives an additional $500 each month in her savings account.

Q: Is Betty's checking account balance always greater than her savings account balance?

A: Yes, based on the analysis, we can conclude that Betty's checking account balance is always greater than her savings account balance.

Q: How can we determine the correct answer to a question like this?

A: To determine the correct answer, we need to analyze the functions C and S and compare the values of the two functions for different values of x.

Q: What is the significance of function C and function S in this context?

A: Function C represents Betty's checking account balance, and function S represents her savings account balance. These functions help us understand how Betty's financial situation changes over time.

Q: Can we use these functions to make predictions about Betty's financial situation in the future?

A: Yes, we can use these functions to make predictions about Betty's financial situation in the future. By analyzing the functions C and S, we can determine how Betty's checking account balance and savings account balance will change over time.

Q: Are there any limitations to using these functions to analyze Betty's financial situation?

A: Yes, there are some limitations to using these functions to analyze Betty's financial situation. For example, these functions do not take into account any interest that may be earned on Betty's savings account or any fees that may be charged on her checking account.

Conclusion

In this Q&A article, we answered some common questions related to Betty's financial situation. We analyzed her checking account balance and savings account balance using functions C and S, respectively. We also determined that Betty's checking account balance is always greater than her savings account balance.

Final Thoughts

Understanding Betty's financial situation using mathematical functions can help us make predictions about her financial situation in the future. However, it is essential to consider any limitations to using these functions, such as interest earned on savings accounts or fees charged on checking accounts.

Additional Resources

For more information on analyzing financial situations using mathematical functions, please refer to the following resources:

[1] "Mathematical Modeling of Financial Systems" by John Wiley & Sons
[2] "Financial Mathematics" by Springer
[3] "Mathematical Finance" by Cambridge University Press

These resources provide a comprehensive overview of mathematical modeling in finance and can be used as a reference for further study.