The Average Annual Salary Of The Employees Of A Company In The Year 2005 Was $\$80,000$. It Increased By The Same Factor Each Year, And By The Year 2006, The Annual Salary Was $\$88,000$. Let $y$ Represent The Average Annual

Introduction

In the year 2005, the average annual salary of employees in a company was $\$80,000$. This figure increased by the same factor each year, and by the year 2006, the annual salary had risen to $\$88,000$. In this article, we will explore the mathematical concept behind this increase and determine the average annual salary of employees in subsequent years.

Understanding the Problem

Let's assume that the average annual salary of employees in the year 2005 is represented by the variable $x$. Since the salary increased by the same factor each year, we can express the average annual salary in the year 2006 as $x \times r$, where $r$ is the common ratio. We are given that the average annual salary in the year 2006 was $\$88,000$, so we can set up the equation:

$$x \times r = 88,000$$

We also know that the average annual salary in the year 2005 was $\$80,000$, so we can set up another equation:

$$x = 80,000$$

Solving for the Common Ratio

Now that we have two equations, we can solve for the common ratio $r$. We can substitute the value of $x$ from the second equation into the first equation:

$$80,000 \times r = 88,000$$

To solve for $r$, we can divide both sides of the equation by $80,000$:

$$r = \frac{88,000}{80,000}$$

$$r = 1.1$$

Determining the Average Annual Salary in Subsequent Years

Now that we have found the common ratio $r$, we can use it to determine the average annual salary of employees in subsequent years. We can start by finding the average annual salary in the year 2007:

$$x \times r^2 = 80,000 \times (1.1)^2$$

$$x \times r^2 = 80,000 \times 1.21$$

$$x \times r^2 = 96,800$$

We can continue this process to find the average annual salary in the year 2008:

$$x \times r^3 = 80,000 \times (1.1)^3$$

$$x \times r^3 = 80,000 \times 1.331$$

$$x \times r^3 = 106,480$$

Calculating the Average Annual Salary in Subsequent Years

We can continue this process to find the average annual salary in subsequent years. Here are the calculations:

Year	Average Annual Salary
2005	$\$80,000$
2006	$\$88,000$
2007	$\$96,800$
2008	$\$106,480$
2009	$\$116,932$
2010	$\$127,823$
2011	$\$139,031$
2012	$\$150,493$
2013	$\$162,231$
2014	$\$174,255$
2015	$\$186,573$

Conclusion

In this article, we have explored the mathematical concept behind the increase in average annual salary of employees in a company. We have determined the common ratio $r$ and used it to calculate the average annual salary in subsequent years. The results show that the average annual salary increases by a factor of 1.1 each year, resulting in a steady increase in salary over time.

References

• [1] "Mathematics for Business and Economics" by John C. Nelson
• [2] "Calculus for Business and Economics" by John C. Nelson

Appendix

Here are the calculations for the average annual salary in subsequent years:

Year	Average Annual Salary
2005	$\$80,000$
2006	$\$88,000$
2007	$\$96,800$
2008	$\$106,480$
2009	$\$116,932$
2010	$\$127,823$
2011	$\$139,031$
2012	$\$150,493$
2013	$\$162,231$
2014	$\$174,255$
2015	$\$186,573$

$$$$

Introduction

In our previous article, we explored the mathematical concept behind the increase in average annual salary of employees in a company. We determined the common ratio $r$ and used it to calculate the average annual salary in subsequent years. In this article, we will answer some frequently asked questions about the average annual salary of employees.

Q: What is the average annual salary of employees in the year 2005?

A: The average annual salary of employees in the year 2005 is $\$80,000$.

Q: What is the common ratio $r$ that determines the increase in average annual salary?

A: The common ratio $r$ is 1.1, which means that the average annual salary increases by 10% each year.

Q: How do you calculate the average annual salary in subsequent years?

A: To calculate the average annual salary in subsequent years, you can use the formula:

$$x \times r^n = 80,000 \times (1.1)^n$$

where $n$ is the number of years after 2005.

Q: What is the average annual salary of employees in the year 2010?

A: To calculate the average annual salary in the year 2010, we can use the formula:

$$x \times r^n = 80,000 \times (1.1)^5$$

$$x \times r^n = 80,000 \times 1.61051$$

$$x \times r^n = 128,840.80$$

So, the average annual salary of employees in the year 2010 is approximately $\$128,841$.

Q: How does the average annual salary change over time?

A: The average annual salary increases by 10% each year, resulting in a steady increase in salary over time.

Q: What is the average annual salary of employees in the year 2020?

A: To calculate the average annual salary in the year 2020, we can use the formula:

$$x \times r^n = 80,000 \times (1.1)^{15}$$

$$x \times r^n = 80,000 \times 4.641588$$

$$x \times r^n = 371,277.04$$

So, the average annual salary of employees in the year 2020 is approximately $\$371,277$.

Q: How can I use this information to make predictions about future salary increases?

A: You can use the formula:

$$x \times r^n = 80,000 \times (1.1)^n$$

to make predictions about future salary increases. Simply plug in the number of years you want to predict and calculate the result.

Conclusion

In this article, we have answered some frequently asked questions about the average annual salary of employees. We have provided formulas and calculations to help you understand how the average annual salary changes over time. We hope this information is helpful in making predictions about future salary increases.

References

• [1] "Mathematics for Business and Economics" by John C. Nelson
• [2] "Calculus for Business and Economics" by John C. Nelson

Appendix

Here are the calculations for the average annual salary in subsequent years:

Year	Average Annual Salary
2005	$\$80,000$
2006	$\$88,000$
2007	$\$96,800$
2008	$\$106,480$
2009	$\$116,932$
2010	$\$128,841$
2011	$\$141,121$
2012	$\$154,051$
2013	$\$167,533$
2014	$\$181,555$
2015	$\$196,141$
2016	$\$211,301$
2017	$\$227,091$
2018	$\$243,531$
2019	$\$260,621$
2020	$\$371,277$

Note: The calculations are based on the common ratio $r = 1.1$ and the initial average annual salary $x = 80,000$.