Question

the median home value in rhode island and colorado (adjusted for inflation) are shown below:

year	rhode island	colorado
2000	133000	166600

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 rhode island in 2010? $ blank
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 blank

question help: message instructor

next question

Explanation:

Part (a)

Step1: Calculate rate for Rhode Island

The time period from 1950 to 2000 is \(2000 - 1950 = 50\) years. The change in value is \(133000 - 59200 = 73800\). The rate \(r_{RI}\) is \(\frac{73800}{50}=1476\) per year.

Step2: Calculate rate for Colorado

The change in value is \(166600 - 43300 = 123300\). The rate \(r_{CO}\) is \(\frac{123300}{50}=2466\) per year.

Step3: Compare rates

Since \(2466>1476\), Colorado has a higher rate.

Step1: Determine the linear equation for Rhode Island

We have two points \((1950, 59200)\) and \((2000, 133000)\). The slope \(m = 1476\) (from part a). Using point - slope form \(y - y_1=m(x - x_1)\), with \((x_1,y_1)=(1950,59200)\), the equation is \(y=1476(x - 1950)+59200\).

Step2: Calculate value in 2010

For \(x = 2010\), \(y=1476(2010 - 1950)+59200=1476\times60 + 59200=88560+59200 = 147760\).

Step1: Write linear equations for both states

For Rhode Island: \(y_{RI}=1476(x - 1950)+59200=1476x-1476\times1950 + 59200=1476x-2878200+59200=1476x - 2819000\)
For Colorado: \(y_{CO}=2466(x - 1950)+43300=2466x-2466\times1950+43300=2466x - 4808700+43300=2466x-4765400\)

Step2: Set equations equal and solve for x

Set \(1476x - 2819000=2466x - 4765400\)
\(4765400 - 2819000=2466x - 1476x\)
\(1946400 = 990x\)
\(x=\frac{1946400}{990}\approx1966.06\)

Answer:

Colorado

Part (b)