Consider two job offers with salaries that increase exponent

Consider two job offers with salaries that increase exponentially.

For Job A, the salary for year 1 is $29,000 while the salary for year 2 will be $31,175.

How many times as large is the salary in Year 2 compared to the salary in Year 1?    

The salary in Year 2 is_____ % of the salary in Year 1. 

What is the percent change in salary from Year 1 to Year 2?  %    

For Job B, the salary for Year 1 is $27,500 while the salary for Year 2 will be $28,600. 

How many times as large is the salary in Year 2 compared to the salary in Year 1?    

The salary in Year 2 is _____% of the salary in Year 1. 

What is the percent change in salary from Year 1 to Year 2?   

You expect to keep this job for at least 5 years and you want to make as much money as possible over the time spent working. Which job should you take?

Job A
Job B

Solution

For Job A, the salary for year 1 is $29,000 while the salary for year 2 will be $31,175.

How many times as large is the salary in Year 2 compared to the salary in Year 1

----> Salary in year2/ salary in year 1 = 31175/29000 = 1.075 times the salary in year1

-----> salary in Year 2 is 1.075 x 100 = 107.5 % of the salary in Year 1

------> percent change in salary from Year 1 to Year 2 =( ( 31175 -29000)/29000)*100

= 7.5%

For Job B, the salary for Year 1 is $27,500 while the salary for Year 2 will be $28,600.

How many times as large is the salary in Year 2 compared to the salary in Year 1?   

----> Salary in year2/ salary in year 1 = 28600/27500 = 1.04 times the salary in year1

-----> salary in Year 2 is 1.04 x 100 = 104 % of the salary in Year 1

------> percent change in salary from Year 1 to Year 2 =( (28600 -27500)/27500)*100

= 4%

------>After five years Job A salary = 29000(1.075)^5 = $41633.25

------>After five years Job B salary = 27500(1.04)^5 = $33457.94

It is better to keep Job A