An employee joined a company in 2009 with a starting

Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen

Problem 22E Chapter 2.4

Discrete Mathematics and Its Applications | 7th Edition

  • 2901 Step-by-step solutions solved by professors and subject experts
  • Get 24/7 help from StudySoup virtual teaching assistants
Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen

Discrete Mathematics and Its Applications | 7th Edition

4 5 0 408 Reviews
22
2
Problem 22E

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.

Step-by-Step Solution:

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,

Step 23 of 43

Chapter 2.4, Problem 22E is Solved
Step 24 of 43

Textbook: Discrete Mathematics and Its Applications
Edition: 7th
Author: Kenneth Rosen
ISBN: 9780073383095

×
Log in to StudySoup
Get Full Access to Discrete Mathematics And Its Applications - 7th Edition - Chapter 2.4 - Problem 22e

Forgot password? Reset password here

Join StudySoup for FREE
Get Full Access to Discrete Mathematics And Its Applications - 7th Edition - Chapter 2.4 - Problem 22e
Join with Email
Already have an account? Login here
Reset your password

I don't want to reset my password

Need help? Contact support

Need an Account? Is not associated with an account
Sign up
We're here to help

Having trouble accessing your account? Let us help you, contact support at +1(510) 944-1054 or support@studysoup.com

Got it, thanks!
Password Reset Request Sent An email has been sent to the email address associated to your account. Follow the link in the email to reset your password. If you're having trouble finding our email please check your spam folder
Got it, thanks!
Already have an Account? Is already in use
Log in
Incorrect Password The password used to log in with this account is incorrect
Try Again

Forgot password? Reset it here