The average annual costs for owning two different refrigerators for x years is given by the two functions: f(x) = 850 + 62x /x a

Question

3 days ago

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The average annual costs for owning two different refrigerators for x years is given by the two functions: f(x) = 850 + 62x /x a

nd g(x) = 1004 + 51x /xIn the long run, the cost of the refrigerator modeled by will be the cheapest, averaging $ per year.

Mathematics

2 answers:

Svet_ta [9.5K] · Answer 1 · 2026-03-24T15:16:00+03:00

Svet_ta [9.5K]3 days ago

6 0

Response:

in part 1: After a year, the cost of the refrigerator represented by f(x) is lower.

in part 2: 14 years

in part 3: g(x)

in part 4: 51

I hope this is useful:)

Inessa [9K] · Answer 2 · 2026-03-24T15:12:19+03:00

In the long term, the expense of the refrigerator represented by g(x) will be the most economical. The average yearly expenditure to operate two different refrigerators over x years is expressed by two functions, f(x) = 850 + 62x and g(x) = 1004 + 51x. Equating these functions, f(x) and g(x) allows us to determine the time in years when their costs will equalize. At x = 1 year, f(1) = 850 + 62 = $912 and g(1) = 1004 + 51 = $1055, indicating f(x) is initially cheaper. To find when f(x) equals g(x), we resolve for x. At x = 14 years, the evaluation shows f(15) = 56.67 + 62 = $118.67 and g(15) = 66.93 + 51 = $117.93, thus confirming g(x) becomes more affordable beyond 14 years. Therefore, for the initial 14 years, f(x) is less than g(x), but thereafter g(x) is cheaper.