Asked by j
The Gordon family plans to buy a TV. One TV has a purchase price of $330 and an estimated yearly operating cost of $14. The other has a purchase price of $369 and an estimated yearly operating cost of $9. Which TV should the Gordons buy if they plan to keep it for 8 years? Use rational functions to help justify your answer.
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Let C1(t) and C2(t) be the total cost after t years.
C1(t) = 330 + 14t (purchase $330 + $14 per year)
C2(t) = 369 + 9t (purchase $369 + $9 per year)
Solve C1(t) = C2(t):
330 + 14t = 369 + 9t → 5t = 39 → t = 7.8 years.
So for t < 7.8 years the $330 TV is cheaper; for t > 7.8 years the $369 TV is cheaper. At t = 8 years:
C1(8) = 330 + 14(8) = 442
C2(8) = 369 + 9(8) = 441
After 8 years the $369 TV costs $441, $1 less than the other. Therefore the Gordons should buy the $369 TV.
C1(t) = 330 + 14t (purchase $330 + $14 per year)
C2(t) = 369 + 9t (purchase $369 + $9 per year)
Solve C1(t) = C2(t):
330 + 14t = 369 + 9t → 5t = 39 → t = 7.8 years.
So for t < 7.8 years the $330 TV is cheaper; for t > 7.8 years the $369 TV is cheaper. At t = 8 years:
C1(8) = 330 + 14(8) = 442
C2(8) = 369 + 9(8) = 441
After 8 years the $369 TV costs $441, $1 less than the other. Therefore the Gordons should buy the $369 TV.
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