the gordon family plans to buy a tv. one tv has a purchase price of $330 and an estimated yearly operating…

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.

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.

Answer

Explanation:

Step1: Define cost - function for first TV

Let $C_1$ be the total cost function for the first TV. The purchase price is $330$ and the yearly operating cost is $14$. For $t$ years, the total cost is the sum of the purchase price and the total operating cost over $t$ years. So, $C_1(t)=330 + 14t$. For $t = 8$ years, $C_1(8)=330+14\times8$. $C_1(8)=330 + 112=442$.

Step2: Define cost - function for second TV

Let $C_2$ be the total cost function for the second TV. The purchase price is $369$ and the yearly operating cost is $9$. For $t$ years, the total cost is $C_2(t)=369+9t$. For $t = 8$ years, $C_2(8)=369 + 9\times8$. $C_2(8)=369+72 = 441$.

Step3: Compare the total costs

Since $C_1(8)=442$ and $C_2(8)=441$, and $441<442$.

Answer:

The Gordons should buy the TV with a purchase price of $369$ and an estimated yearly operating cost of $9$.