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.

SOLUTIONStep 1In this question,it is given that an employee joined in 2009 with a starting salary of $50.000,gets an increment of $1000 plus 5% of the salary of the previous year.We are asked to find the following cases.Step 21) a recurrence relation for the salary of this employee n years after 2009.The recurrence relation for the salary for the nth year is for and Step 32) the salary of the employ in 2017.The employee joined in 2009 and we need to calculate the salary of 2017.Therefore .Thus we need to calculate .According to the step 1 we have the recurrence relation Thus we get Therefore the salary of the employee in 2017 is Step 43) an explicit formula for the salary of the employee after n years from 2009.We can see that this is a nonhomogeneous recurrence relation.The solution for a nonhomogeneous recurrence relation is The formula for Let Therefore we have since Therefore we have the general solution for the non homogeneous equation,