An employee joined a company in 2020 with a starting salary of $60,000. Every year, the employee receives a raise of $2,000 plus 3% of the salary of the previous year.

(a) Set up a recurrence relation.

A. [tex]S_n = S_{n-1} + 2000 + 0.03 S_{n-1}[/tex]

B. [tex]S_n = S_{n-1} + 2000 + 0.03 S_n[/tex]

C. [tex]S_n = S_{n-1} + 60000 + 0.03 S_n[/tex]

D. [tex]S_n = S_{n-1} + 60000 + 0.03 S_{n-1}[/tex]

The correct recurrence relation for calculating the employee's annual salary with an annual raise is Sₙ = S_(n-1) + 2000 + 0.03 S_(n-1), which includes both a fixed raise and a percentage of the previous year's salary. So, the correct option is b) Sₙ = S_(n-1) + 2000 + 0.03 Sₙ

Explanation:

The recurrence relation for an employee's salary in this scenario would be based on the increase in salary due to both a fixed raise and a percentage of the previous year's salary. Every year, the employee gets a raise of $2,000 plus 3% of the salary from the previous year. Thus, the correct recurrence relation from the options provided is Sₙ = S_(n-1) + 2000 + 0.03 S_(n-1), indicating that the next year's salary (Sₙ) is equal to the previous year's salary (S_(n-1)) plus a $2,000 increase and an additional 3% of the previous year's salary.