# Comparing Salary Structures

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Calcmath
ATTACHED FILE(S)
Comparing Two Salary Structures
PROBLEM SITUATION:
You have two job offers. Job 1 has an annual starting salary of \$60,000 with the expectation of a \$1000 raise each year. Job 2 has an annual starting salary of \$45,000 and expectation of a 7.5% annual raise.
(3pts) 1. Tables of future annual salaries can be used to begin to compare the two job offers. Copy the following tables into your report and complete them.Round to the nearest dollar.
TABLE 1 TABLE 2

Job 1:Annual Salary

Job 2: Annual Salary

# of Years Worked

Annual Salary after t years

Successive
Differences

Successive Ratios
(3 decimal places)

# of Years Worked

Annual Salary after t years

Successive
Differences

Successive Ratios
(3 decimal places)

0

Salary of year 1 – salary of year 0

Salary or year 1/
salary of year 0

0

Salary of year 1 – salary of year 0

Salary or year 1/
salary of year 0

1

1

2

2

3

3

4

4

5

5

6

6

(1 pt ea) 2.Write the answers to questions a, b, and c using complete sentences. For question d, just write the function rule.
a. In which table are the successive differences constant?
b. What is that constant difference?
c. What type of function can be used to model this salary offer?
d. Write the function rule that gives the annual salary after t years on the job.
(1 pt ea) 3.Write the answers to questions a, b, and c using complete sentences. For question d, just write the function rule.

a. In which table are the successive ratios constant?
b. What is that constant ratio?
c. What type of function can be used to model this salary offer?
d. Write the function rule that gives the annual salary after t years on the job.
(4pts) 4.Use your calculator to produce, in the same window, the graphs of both salary functions (From questions 2d and 3d) over the domain 0 to 100 years and a range 0 to 130,000
You can take a picture of your graph with your phone.Email a copy of the picture to yourself.Print the picture and add to the end of your project. I will not accept hand-drawn graphs.
(4pts) 5.Use your graphing calculator to determine the number of years must you work in order for the annual salary of Job 2 to equal the corresponding annual salary of Job 1?You can take a picture of your graph with your phone.Email a copy of the picture to yourself.Print the picture and add to the end of your project. I will not accept hand-drawn graphs.How many years must you work to have the annual salary of Job 1 to equal Job 2?
(1pts) 6a. What equation can be solved to find the number of years it will take to double the starting salary for Job 1?
(2pts) b. Solve the equation algebraically (show the steps).
(4pts) c. Check your solution from part b graphically. Using your smartphone, take a picture of the graph from your calculator.You can take a picture of your graph with your phone.Email a copy of the picture to yourself.Print the picture and add to the end of your project.I will not accept hand-drawn graphs.
(1pts) d. Write your solution in sentence form.
(2pts) 7a.What equation can be solved to find the number of years it will take to double the starting salary for Job 2?
(4pts) b. Solve the equation graphically. You can take a picture of your graph with your phone.Email a copy of the picture to yourself.Print the picture and add to the end of your project.I will not accept hand-drawn graphs.
(1pts) c. Write your solution in sentence form.
(4pts) 8. In comparing the earning power of the job offers, one might be interested in the cumulative earnings, that is, the sum total earnings for all the years worked in the chosen job. TABLE 3 below gives cumulative earnings for both job offers for the given number of years worked. For example, when t = 8, the table gives.That means, after working 8 years in Job 1, the total earnings is \$508,000.
Note that the last column gives a comparison of the cumulative earnings of both jobs for the same number of years worked by calculating the difference.
Complete the table below.
TABLE 3

Comparison of Cumulative Earnings

t = # of Years Worked

= Cumulative Earnings after t years on Job 1

= Cumulative Earnings after t years on Job 2

Difference in Cumulative Earnings:

1

\$60,000

\$ 45,000

\$15,000

2

\$121,000

\$ 93,375

\$27,625

3

4

5

6

7

8

\$508,000

\$470,087

\$37,913

9

\$576,000

\$550,343

\$25,657

10

\$645,000

\$636,619

\$8,381

11

\$715,000

\$729,365

\$(14,365)
(1pts) 9a. The ordered pair occurs in the TABLE 1.Explain the meaning of this ordered pair in the context of the situation.
(1pts) b. The ordered pair occurs in the TABLE 3.Explain the meaning of this ordered pair in the context of the situation.
(1pts) c. The ordered pair occurs in the TABLE 3.Explain the meaning of this ordered pair in the context of the situation.

(2pts) 10 How many years must you work in order for the cumulative salary of Job 2 to be higher than the cumulative salary for Job 1?Explain how TABLE 3 gives this information.
(5pts) 11.You would like to see the cumulative salary for each job after 20 years and wish you had function rules for and .Your math major friend develops the following:and.Use these function rules to find the cumulative salaries after 20 years.Show your calculations. Comment on your findings.
(2pts) 12. Write a well thought out paragraph that compares the pros and cons of each of the salary offers and indicates which job offer he/she would accept and why.The information learned from all the tables should be incorporated into the analysis. Assume that except for the salary structure, the two jobs are equal (same commute, same benefits, etc.).

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