An employee joined a company in 2009 with a starting salary of $50,000. Every year this employee receives a raise of $1000 plus 5% of the salary of the previous year.
a) Set up a recurrence relation for the salary of this employee n years after 2009.
b) What will the salary of this employee be in 2017?
c) Find an explicit formula for the salary of this employee n years after 2009.

(a) The required recurrence relation for  the salary of the employee of n years after 2009 is .

(b)The salary of the employee will be $83421.88 in 2017.

(c)

Step-by-step explanation:

Summation of a G.P series

(a)

Every year the salary is increasing 5% of the salary of the previous year plus $1000.

Let represents the salary of the employee of n years after 2009.

Then represents the salary of the employee of (n-1) years after 2009.

Then

The required recurrence relation for  the salary of the employee of n years after 2009 is .

(b)

Given,

Since 2017 is 8 years after 2009.

So, n=8.

∴

≈$83421.88

The salary of the employee will be $83421.88 in 2017.

(c)

Given,

We successively apply the recurrence relation

                    ...............................

                   .................................

i belive those are the ones that are under 90 degreese.