Get comprehensive answers to your questions with the help of IDNLearn.com's community. Ask your questions and receive reliable and comprehensive answers from our dedicated community of professionals.
Sagot :
Let's address each part of the problem step by step.
### 1. Create an equation for each situation
For Job A:
- Initial salary: \[tex]$75,000 - Annual raise: \$[/tex]5,000 after the first year
The salary for Job A after [tex]\( n \)[/tex] years can be represented as:
[tex]\[ S_A(n) = 75000 + 5000n \][/tex]
For Job B:
- Initial salary: \[tex]$55,000 - Annual raise: 8% of the previous year's salary The salary for Job B after \( n \) years can be expressed as: \[ S_B(n) = 55000 \times (1 + 0.08)^n \] ### 2. Use each equation to complete the table We will calculate the salaries for both jobs over the first 10 years. | Year | Job A Salary (\$[/tex]) | Job B Salary (\[tex]$) | |------|--------------------|----------------------------| | 1 | 80,000 | 59,400 | | 2 | 85,000 | 64,152 | | 3 | 90,000 | 69,284.16 | | 4 | 95,000 | 74,826.89 | | 5 | 100,000 | 80,813.04 | | 6 | 105,000 | 87,278.09 | | 7 | 110,000 | 94,260.33 | | 8 | 115,000 | 101,801.16 | | 9 | 120,000 | 109,945.25 | | 10 | 125,000 | 118,740.87 | These values are computed using the given equations. ### 3. When will Job B earn more than Job A? To determine when Job B's salary will exceed Job A's salary, we need to compare the salaries year by year. From the table: - In year 1, Job A: \$[/tex]80,000, Job B: \[tex]$59,400 - In year 2, Job A: \$[/tex]85,000, Job B: \[tex]$64,152 - In year 3, Job A: \$[/tex]90,000, Job B: \[tex]$69,284.16 - In year 4, Job A: \$[/tex]95,000, Job B: \[tex]$74,826.89 - In year 5, Job A: \$[/tex]100,000, Job B: \[tex]$80,813.04 - In year 6, Job A: \$[/tex]105,000, Job B: \[tex]$87,278.09 - In year 7, Job A: \$[/tex]110,000, Job B: \[tex]$94,260.33 - In year 8, Job A: \$[/tex]115,000, Job B: \[tex]$101,801.16 - In year 9, Job A: \$[/tex]120,000, Job B: \[tex]$109,945.25 - In year 10, Job A: \$[/tex]125,000, Job B: \[tex]$118,740.87 We observe that throughout this 10-year period, Job B's salary never exceeds Job A's salary. Job B's salary continues to increase but does not surpass Job A's salary within these 10 years. ### 4. Which job would you choose and why? Given the observations from the table and the comparison over the 10 years: - Job A starts at \$[/tex]75,000 and increases by \[tex]$5,000 each year. - Job B starts at \$[/tex]55,000 with an 8% annual raise but does not exceed Job A's salary within the first 10 years.
Based on this data, I would choose Job A because Job A consistently offers a higher salary compared to Job B over the provided 10-year period. This higher consistent salary from Job A could lead to better financial stability and higher overall earnings in this timeframe.
### 1. Create an equation for each situation
For Job A:
- Initial salary: \[tex]$75,000 - Annual raise: \$[/tex]5,000 after the first year
The salary for Job A after [tex]\( n \)[/tex] years can be represented as:
[tex]\[ S_A(n) = 75000 + 5000n \][/tex]
For Job B:
- Initial salary: \[tex]$55,000 - Annual raise: 8% of the previous year's salary The salary for Job B after \( n \) years can be expressed as: \[ S_B(n) = 55000 \times (1 + 0.08)^n \] ### 2. Use each equation to complete the table We will calculate the salaries for both jobs over the first 10 years. | Year | Job A Salary (\$[/tex]) | Job B Salary (\[tex]$) | |------|--------------------|----------------------------| | 1 | 80,000 | 59,400 | | 2 | 85,000 | 64,152 | | 3 | 90,000 | 69,284.16 | | 4 | 95,000 | 74,826.89 | | 5 | 100,000 | 80,813.04 | | 6 | 105,000 | 87,278.09 | | 7 | 110,000 | 94,260.33 | | 8 | 115,000 | 101,801.16 | | 9 | 120,000 | 109,945.25 | | 10 | 125,000 | 118,740.87 | These values are computed using the given equations. ### 3. When will Job B earn more than Job A? To determine when Job B's salary will exceed Job A's salary, we need to compare the salaries year by year. From the table: - In year 1, Job A: \$[/tex]80,000, Job B: \[tex]$59,400 - In year 2, Job A: \$[/tex]85,000, Job B: \[tex]$64,152 - In year 3, Job A: \$[/tex]90,000, Job B: \[tex]$69,284.16 - In year 4, Job A: \$[/tex]95,000, Job B: \[tex]$74,826.89 - In year 5, Job A: \$[/tex]100,000, Job B: \[tex]$80,813.04 - In year 6, Job A: \$[/tex]105,000, Job B: \[tex]$87,278.09 - In year 7, Job A: \$[/tex]110,000, Job B: \[tex]$94,260.33 - In year 8, Job A: \$[/tex]115,000, Job B: \[tex]$101,801.16 - In year 9, Job A: \$[/tex]120,000, Job B: \[tex]$109,945.25 - In year 10, Job A: \$[/tex]125,000, Job B: \[tex]$118,740.87 We observe that throughout this 10-year period, Job B's salary never exceeds Job A's salary. Job B's salary continues to increase but does not surpass Job A's salary within these 10 years. ### 4. Which job would you choose and why? Given the observations from the table and the comparison over the 10 years: - Job A starts at \$[/tex]75,000 and increases by \[tex]$5,000 each year. - Job B starts at \$[/tex]55,000 with an 8% annual raise but does not exceed Job A's salary within the first 10 years.
Based on this data, I would choose Job A because Job A consistently offers a higher salary compared to Job B over the provided 10-year period. This higher consistent salary from Job A could lead to better financial stability and higher overall earnings in this timeframe.
Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. Discover the answers you need at IDNLearn.com. Thank you for visiting, and we hope to see you again for more solutions.
