Respuesta :
Given
cost of an LCD TV dropped from $800 in 2012 to $700 in 2014
Find out unit rate at which the cost has been decreasing
Proof of (1)
As given in the question
let x denote the number of year and y denote the cost of the LCD TV
Take 2012 as intial year
cost of LCD TV = $800
Thus
x = 0 , y = 800
Take 2014 as the final year.
cost of LCD TV = $700
y = 700
x =2
( as the year changes 2012 to 2014 here exit change of 2 years)
Now find out the unit rate at which the cost is decreasing.
Take two points
( 0, 800) and ( 2, 700)
[tex]unit\ rate=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
putting the above value
we get
[tex]unit\ rate=\frac{700-800}{2-0}\\unit\ rate=\frac{-100}{2}[/tex]
thus
unit rate = -50
unit rate at which the cost has been decreasing is -50.
proof of ( 2)
points are( 0, 800) and ( 2, 700)
The equation is
[tex]\left ( y - y_1 \right ) =\frac{y_2 - y_1}{x_2-x_1}(x-x_1)[/tex]
put the values in the above equation
[tex]\left ( y - 800 \right ) =\frac{700 - 800}{2-0}(x-0)[/tex]
thus the equation becomes
y = -50x+800
Thus y = -50x+800 is the linear model to perdict the cost of LCD TV.
Now find out cost of the LCD TV in 2016
As taken earlier 2012 as the intial year
find the cost of LCD TV in 2016
thus x =4
( year changes 2012 to 2016 here exit the change of 4 years)
put x = 4 in the linear model y = -50x + 800
y = -50× 4 + 800
y = -200 + 800
y = 600
The cost of the LCD TV in 2016 is $600.
Hence proved.
