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.
