Algebra and Trigonometry (6th Edition)
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ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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![### Median Home Value Trends in West Virginia and Rhode Island
The table below shows the median home values (adjusted for inflation) in West Virginia and Rhode Island for the years 1950 and 2000.
| Year | West Virginia | Rhode Island |
|------|---------------|--------------|
| 1950 | $33,200 | $59,200 |
| 2000 | $72,800 | $133,000 |
### Analysis and Discussion
#### Assuming Home Values Change Linearly:
a) **Rate of Increase in Home Values:**
* Determine in which state the home values have increased at a higher rate.
b) **Projected Home Value in West Virginia for 2010:**
* Estimate the median home value in West Virginia in 2010 assuming the trends continue linearly.
c) **Equal Median Home Values Year Projection:**
* Identify the year when the median home values in both states would be equal if the linear trend existed before 1950 and continues after 2000. (Note: The answer might be far-fetched or unrealistic).
Use the data provided to answer these questions.
### Calculations:
For part a, calculate the rate of increase for each state using the formula:
\[ \text{Rate of increase} = \frac{\text{Value in 2000} - \text{Value in 1950}}{2000 - 1950} \]
For part b, extend the linear trend to 2010 for West Virginia using the calculated rate of increase.
For part c, solve for the year in which the projected values of both states are equal, using their respective rates of increase.
### Conclusion
Answer the questions based on the data and calculations to understand the trends in home value changes over time in West Virginia and Rhode Island. This exercise helps in understanding linear trends and making future projections based on historical data.
---
This content is designed to accompany an educational module on linear trends and projections, providing students with the opportunity to apply mathematical concepts to real-world data.](https://content.bartleby.com/qna-images/question/88d18a19-21f4-41fb-afe0-306734676977/f637d023-cb2e-4bab-b239-20addda7c6e0/vxge5mq.jpeg)
Transcribed Image Text:### Median Home Value Trends in West Virginia and Rhode Island
The table below shows the median home values (adjusted for inflation) in West Virginia and Rhode Island for the years 1950 and 2000.
| Year | West Virginia | Rhode Island |
|------|---------------|--------------|
| 1950 | $33,200 | $59,200 |
| 2000 | $72,800 | $133,000 |
### Analysis and Discussion
#### Assuming Home Values Change Linearly:
a) **Rate of Increase in Home Values:**
* Determine in which state the home values have increased at a higher rate.
b) **Projected Home Value in West Virginia for 2010:**
* Estimate the median home value in West Virginia in 2010 assuming the trends continue linearly.
c) **Equal Median Home Values Year Projection:**
* Identify the year when the median home values in both states would be equal if the linear trend existed before 1950 and continues after 2000. (Note: The answer might be far-fetched or unrealistic).
Use the data provided to answer these questions.
### Calculations:
For part a, calculate the rate of increase for each state using the formula:
\[ \text{Rate of increase} = \frac{\text{Value in 2000} - \text{Value in 1950}}{2000 - 1950} \]
For part b, extend the linear trend to 2010 for West Virginia using the calculated rate of increase.
For part c, solve for the year in which the projected values of both states are equal, using their respective rates of increase.
### Conclusion
Answer the questions based on the data and calculations to understand the trends in home value changes over time in West Virginia and Rhode Island. This exercise helps in understanding linear trends and making future projections based on historical data.
---
This content is designed to accompany an educational module on linear trends and projections, providing students with the opportunity to apply mathematical concepts to real-world data.
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