Question

Jamal is offered two jobs. The first job offers a starting salary of $25,000 that increases by $800 each year he is with the company. The second job offers a starting salary of $23,000 that increases by 3.2% each year he is with the company. After how many years will the salary of the second job surpass the salary of the first?

Answer 1

Answer:

  16 years

Step-by-step explanation:

If the salary at the first job is modeled by ...

  y1 = 25000 +800x . . . . . salary after x years

and that of the second job is modeled by ...

  y2 = 23000(1.032^x)

The salaries will be equal when ...

  y2 = y1

  23000(1.032^x) = 25000 +800x

There are no algebraic methods for solving an equation like this. However, a graphing calculator can give a pretty good estimate of the solution. It shows us that the equations give the same salary after about 15.3 years. If raises are given once per year, then ...

  the salary of the second job will surpass the salary of the first job after 16 years.

_____

Additional comments

It isn't until after more than 25 years that total earnings at the second job exceed those at the first job. That time period is even longer if the effect of inflation is taken into account.

A spreadsheet can also provide a good answer to this question, either by listing the yearly salaries in a table, or by searching for a value of x that will make the salaries the same.