if we assume the linear trend existed before 1950 and continues after 2000, the two states’ median house values wil be (or were) equal in what year? (The answer might be absurd.)

To find the year two states would theoretically have equal median house values, one could use provided growth rates and starting house values to set up an equation and solve for time. However, assuming a linear trend can lead to inaccurate results as real estate markets are affected by many fluctuating factors.

To calculate the year in which two states would have theoretically had equal median house values, we first need to know the starting house values for each state and the annual growth rate trends. We've learned from the FRED® Economic Data that median sales price for a home in the U.S. was $122,900 in 1990 and rose to $232,000 by the end of 2016, an average growth rate of 3.1% annually. In other periods, such as the 1970s, 1980s, and 1990s, housing prices increased about 6% per year on average. During the 'housing bubble' years (2003-2005), they experienced a sharp rise and then a fall with the 2007-2008 recession.

Assuming linear trend (constant growth), we would set up an equation with these variables and solve for the year (time) where the values are equal. However, do kindly note that assuming the same trend can often lead to absurd results as housing markets are affected by a variety of economic, political, and demographic factors and do not always follow a linear trend.

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a) Home values have increased at a higher rate in New York.

b) The median home value in Arkansas in 2010 would be $82,400.

c) The two states' median house values were equal in year = 190

Let’s break down each question:

a) To determine which state’s home values have increased at a higher rate, we need to calculate the rate of change for each state. The rate of change is calculated as the difference in home values divided by the difference in years.

For Arkansas, the rate of change is (72,800 - 24,800) / (2000 - 1950) = $960 per year.

For New York, the rate of change is (148,700 - 61,500) / (2000 - 1950) = $1,744 per year.

So, home values have increased at a higher rate in New York.

b) If these trends were to continue, the median home value in Arkansas in 2010 would be the 2000 home value plus the rate of change times the number of years since 2000.

So, the median home value in Arkansas in 2010 would be 72,800 + $960 * (2010 - 2000) = $82,400.

c) If we assume the linear trend existed before 1950 and continues after 2000, the two states’ median house values will be equal when the equation for Arkansas’s home values equals the equation for New York’s home values.

We are given that the median home value in Arkansas in 1950 was $24,800 and in 2000 it was $72,800. This gives us a rate of increase of $960 per year. So, the value of a home in Arkansas in year ‘x’ can be represented by the equation:

[tex]V_{Arkansas}(x) = 24800 + 960 * (x - 1950)[/tex]

Similarly, the median home value in New York in 1950 was $61,500 and in 2000 it was $148,700. This gives us a rate of increase of $1,744 per year. So, the value of a home in New York in year ‘x’ can be represented by the equation:

[tex]V_{NewYork}(x) = 61500 + 1744 * (x - 1950)[/tex]

The two states’ median house values will be equal when

[tex]V_{Arkansas}(x) = V_{NewYork}(x)[/tex]

Setting the two equations equal to each other and solving for ‘x’ gives us:

[tex]24800 + 960 * (x - 1950) = 61500 + 1744 * (x - 1950)[/tex]

[tex]24800+960x-1872000=61500+1744x-3400800\\784x=149100\\x=190.17[/tex]

We round it to the nearest whole number because it represents a year.

So, the two states' median house values were equal in year = 190

Complete Question:

The median home value in Arkansas and New York (adjusted for inflation) are shown below:

Year Arkansas  New York

1950 24,800 61,500

2000 72,800 148,700

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 Arkansas 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)

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