The cost of an lcd tv dropped from $800 in 2012 to $700 in 2014. (i) find the unit rate at which the cost has been decreasing. (express your answer rounded correctly to the nearest cent! ) dollars per year (ii) construct a linear model to predict the cost of an lcd tv and use it to predict the cost of a tv in 2016. (express your answer rounded correctly to the nearest cent! )

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)

putting the above value

we get

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

put the values in the above equation

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.

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