Question

the median home value in iowa and maryland (adjusted for inflation) are shown below.

year	iowa	maryland
2000	82500	146000

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 iowa 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 i
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Explanation:

Step1: Calculate the rate of increase for Iowa

The formula for the rate of change (slope) of a linear function is $m=\frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1,y_1)$ and $(x_2,y_2)$ are two points. For Iowa, $x_1 = 1950$, $y_1=38300$, $x_2 = 2000$, $y_2 = 82500$. Then $m_{Iowa}=\frac{82500 - 38300}{2000 - 1950}=\frac{44200}{50}=884$.

Step2: Calculate the rate of increase for Maryland

For Maryland, $x_1 = 1950$, $y_1 = 48700$, $x_2=2000$, $y_2 = 146000$. Then $m_{Maryland}=\frac{146000 - 48700}{2000 - 1950}=\frac{97300}{50}=1946$. Since $1946>884$, Maryland has a higher - rate of increase.

Step3: Find the linear equation for Iowa

The point - slope form of a line is $y - y_1=m(x - x_1)$. Using the point $(1950,38300)$ and $m = 884$, we have $y-38300=884(x - 1950)$. For $x = 2010$, $y-38300=884(2010 - 1950)$, $y-38300=884\times60$, $y=38300+53040=91340$.

Step4: Find the linear equations for both states and solve for when they are equal

The linear equation for Iowa is $y_{Iowa}=884(x - 1950)+38300=884x-884\times1950 + 38300=884x-1723800+38300=884x - 1685500$. The linear equation for Maryland is $y_{Maryland}=1946(x - 1950)+48700=1946x-1946\times1950 + 48700=1946x-3794700+48700=1946x - 3746000$. Set $y_{Iowa}=y_{Maryland}$, then $884x - 1685500=1946x - 3746000$. Rearranging gives $3746000 - 1685500=1946x - 884x$, $2060500 = 1062x$, $x=\frac{2060500}{1062}\approx1940.21$.

Answer:

a) Maryland
b) $91340$
c) $1940$ (rounded to the nearest whole - year)