Question

the median home value in missouri and wyoming (adjusted for inflation) are shown below:

year	missouri	wyoming
2000	89900	96600

if we assume that the house values are changing linearly,
a) in which state have home values increased at a higher rate? select an answer
b) if these trends were to continue, what would be the median home value in missouri in 2010? $$
$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
question help: video

Explanation:

Step1: Calculate the rate of increase for Missouri

The rate of change formula for a linear function is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $x$ be the year and $y$ be the home - value. For Missouri, $x_1 = 1950$, $y_1=38800$, $x_2 = 2000$, $y_2 = 89900$. Then $m_{MO}=\frac{89900 - 38800}{2000 - 1950}=\frac{51100}{50}=1022$.

Step2: Calculate the rate of increase for Wyoming

For Wyoming, $x_1 = 1950$, $y_1 = 41300$, $x_2 = 2000$, $y_2 = 96600$. Then $m_{WY}=\frac{96600 - 41300}{2000 - 1950}=\frac{55300}{50}=1106$. Since $1106>1022$, Wyoming has a higher rate of increase.

Step3: Find the median home - value in Missouri in 2010

The linear equation for Missouri is $y - y_1=m_{MO}(x - x_1)$. Using the point $(1950,38800)$ and $m_{MO}=1022$, for $x = 2010$, we have $y-38800=1022\times(2010 - 1950)$. So $y=38800+1022\times60=38800 + 61320=100120$.

Step4: Find the year when the two states' median home - values are equal

The linear equation for Missouri is $y_{MO}=1022(x - 1950)+38800=1022x-1022\times1950 + 38800=1022x-1992900+38800=1022x - 1954100$. The linear equation for Wyoming is $y_{WY}=1106(x - 1950)+41300=1106x-1106\times1950 + 41300=1106x-2156700+41300=1106x - 2115400$. Set $y_{MO}=y_{WY}$, then $1022x - 1954100=1106x - 2115400$. Rearranging gives $1106x-1022x=2115400 - 1954100$, $84x = 161300$, and $x=\frac{161300}{84}\approx1920.24$.

Answer:

a) Wyoming
b) 100120
c) 1920.24 (approx)