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

Question

Kathy Gallegos

Mathematics

5 January, 00:19

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

+5

Answers (1)

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Grace Robinson · Answer 1

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