Question

A refrigerator costs $850. The estimated yearly operating cost of the refrigerator is $62. Which rational function models the average annual cost, in dollars, of the refrigerator if it is kept for x years?

a) f(x)=850+62/x
b) f(x)=850/x+62
c) f(x)=850+62x/x
s) f(x)=850/x×62

Answer 1

The rational function that models the average annual cost of the refrigerator over x years is f(x) = 850/x + 62, which includes the initial cost spread over x years plus the constant yearly operating cost.

Step-by-step explanation:

To model the average annual cost of the refrigerator over x years, we need to consider both the initial cost and the yearly operating cost. The initial cost of the refrigerator is a one-time expense, while the operating cost is a recurring expense each year.

The correct rational function to model the average annual cost is f(x) = \frac{850}{x} + 62. This function divides the initial cost of $850 by the number of years the refrigerator is kept, which gives the average annual cost for the initial purchase, and then adds the estimated yearly operating cost of $62.

Thus, the longer the refrigerator is kept, the less the average annual cost of the initial purchase will be, as it's spread out over more years. The operating cost remains constant each year. By calculating this function for different values of x, you can determine how the average annual cost decreases over time.