Every year, Alice gets a raise of $3,000 plus 6% of her previous year's salary.

Question

Every year, Alice gets a raise of $3,000 plus 6% of her previous year's salary. Her starting salary is $20,000. Give a recurrence relation for S(n), Alice's salary after n years, for n ≥ 0.

S(n) =
if n = 0
+ · S(n − 1) if n > 0

Answer 1

S(0) is her first salary which is $20,000

S(1) would be her next salary.

To find this , we take her previous salary ($20,000) and add 6% (.06*$20,000)+$3,000

This is equivalent to S(1)=S(0)+.06(S(0))+3,000

This will continue for all years n>0

S(0) is S(1-1)

So for the recurring relation, her salary for year S(n)= 1.06*S(n-1)+3,000 ;S(0)= $20,000