The median home value in Kentucky and Colorado adjusted for

The median home value in Kentucky and Colorado (adjusted for inflation) are shown below. If we assume that the house values are changing linearly, a) In which state have home values increased at a higher rate? b) If these trends were to continue, what would be the median home value in Kentucky in 2010? exist c) If we assume the linear trend existed before 1950 and continues after 2000, the two states\' median house values will be (or were) equal in what year? (The answer might be absurd) The year

Solution

assuming 1950 as x = 0 . 2000 = 50 , 2010 = 60

rate of change in Kentucky is ( 0, 32000) and ( 50 , 86700 )

rate of change = (86700 - 32000) / 50 = 1094

rate of change in Colorado is ( 0 , 43300 ) and ( 50 , 166600)

rate of change = ( 166600 - 43300 ) / 50

= 2466

therefore, in Colorado the values have increased at a higher rate

b) equation for Kentucky is y = 1094 x + 32000

in 2010 value would be

y = 1094(60) + 32000

y = 97640

c) Kentucky increased 54700 in 50 years

Colorado increased 79900 in 50 years

54700x + 32000 = 79900x + 86700

-25200x = 54700

x = -2.17

so they were equal 2.17* 50 = 108.5

1950 - 108.5 = 1841.5

they were equal in the year 1842