Q:

Adrian's annual income changes every year because of the following three factors: On average, his salary is 1.2 times the previous year's salary. 30% of his income is budgeted for rent. In addition to his salary, Adrian's income increases by $2,300 each year as a result of gifts from family members. If Adrian initially has $52,000 and n denotes the number of years, which recursive equation gives Adrian's annual income as a function of the year, f(n)?

Accepted Solution

A:
In this question, Adrian initially has $52,000 and his salary is 1.2 times the previous year's salary. This means the income should look like this:52000*1.2^n 

30% of his income is budgeted for rent, then the equation should look like this: 30% * income= 30%*(52000*1.2^n)

Adrian's income increases by $2,300 each year as a result of gifts will make this equation:2300n

if you put the 3 equation together you will get
f(n)= 52000*1.2^n - 0.3(52000*1.2^n) +2300n
f(n)= 36400*1.2^n +2300n