Question

The average annual costs for owning two different refrigerators for x years is given by the two functions: f(x) = 850 + 62x /x and g(x) = 1004 + 51x /xIn the long run, the cost of the refrigerator modeled by will be the cheapest, averaging $ per year.

Answer 1

Answer:

part 1: After one year, the cost of the refrigerator modeled by f(x) is cheaper.

part 2: 14 years

part 3: g(x)

part 4: 51

hope this helps :)

Answer 2

Answer:

In the long run cost of the refrigerator g(x) will be cheaper.

Step-by-step explanation:

The average annual cost for owning two different refrigerators for x years is given by two functions

f(x) = $\frac{850+62x}{x}$

     = $\frac{850}{x}+62$

and g(x) = $\frac{1004+51x}{x}$

             = $\frac{1004}{x}+51$

If we equate these functions f(x) and g(x), value of x (time in years) will be the time by which the cost of the refrigerators will be equal.

At x = 1 year

f(1) = 850 + 62 = $912

g(1) = 1004 + 51 = $1055

So initially f(x) will be cheaper.

For f(x) = g(x)

$\frac{850}{x}+62$ = $\frac{1004}{x}+51$

$\frac{1004}{x}-\frac{850}{x}=1004-850$

$\frac{154}{x}=11$

x = $\frac{154}{11}=14$

Now f(15) = 56.67 + 62 = $118.67

and g(x) = 66.93 + 51 = $117.93

So g(x) will be cheaper than f(x) after 14 years.

This tells below 14 years f(x) will be less g(x) but after 14 years cost g(x) will be cheaper than f(x).