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)?

f(1) = 52,000; f(n) = 1.2 · f(n - 1) - 0.30 · f(n - 1) + 2,300; for n ≥ 2

f(1) = 52,000; f(n) = 1.2 · f(n - 1) + 0.30 · f(n - 1) + 2,300; for n ≥ 2

f(1) = 52,000; f(n) = 0.3 · f(n - 1) - 1.2 · f(n - 1) + 2,300; for n ≥ 2

f(1) = 52,000; f(n) = 0.3 · f(n - 1) + 1.2 · f(n - 1) + 2,300; for n ≥ 2

Respuesta :

On average, his salary is 1.2 times the previous year's salary:
f(n)=1.2*f(n-1)

30% of his income is budgeted for rent:
Rent: R=30%f(n-1)=30*f(n-1)/100→R=0.30*f(n-1)

In addition to his salary, Adrian's income increases by $2,300 each year as a result of gifts from family members:
Gifts: G=2,300

If Adrian initially has $52,000:
n=1, f(n)=f(1)=52,000

If n denotes the number of years, which recursive equation gives Adrian's annual income as a function of the year, f(n)?
f(1)=52,000
f(n)=1.2*f(n-1)-R+G; 
for n ≥ 2
f(n)=1.2*f(n-1)-0.30*f(n-1)+2,300; for n ≥ 2

Answer: First option:
f(1) = 52,000; f(n) = 1.2 · f(n - 1) - 0.30 · f(n - 1) + 2,300; for n ≥ 2