Respuesta :
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) = [tex]\frac{850+62x}{x}[/tex]
= [tex]\frac{850}{x}+62[/tex]
and g(x) = [tex]\frac{1004+51x}{x}[/tex]
= [tex]\frac{1004}{x}+51[/tex]
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)
[tex]\frac{850}{x}+62[/tex] = [tex]\frac{1004}{x}+51[/tex]
[tex]\frac{1004}{x}-\frac{850}{x}=1004-850[/tex]
[tex]\frac{154}{x}=11[/tex]
x = [tex]\frac{154}{11}=14[/tex]
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).
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 :)
