Linear Models -
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Linear Models - |
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| The Real Estate Agent Problem
The (average) sale price for a single family property
in Somers and Poughkeepsie is tabulated below:
(a) Find a linear model relating the year x and the sales price y for a single family property in Somers. (a) Find a linear model relating the year x and the sales price y for a single family property in Poughkeepsie. (c) Sketch the graph of both modeling equations in a common coordinate
system; restrict your attention to (d) What is the sales price in Somers and Poughkeepsie in 1983 and 1998? (e) When will the sales price in Somers and Poughkeepsie we equal and what is this price? (f) When will the average sales price in Poughkeepsie be $15,000 less than Somers sales price? What are the two sales prices at this time? (g) When will the Poughkeepsie be $15,000 more than the Somers sales price? What are the two sales prices at this time? (h) When will the Somers sales price be double the Poughkeepsie sales price? (i) Is the Poughkeepsie sales price ever double the Somers sales price? Explain your answer.? |
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| Hints:
1. Use info in table to find two linear models, one for Somers, y1, and one for Poughkeepsie, y2. 2. For each models determine the slope and y-intercepts to find their corresponding formulas: e.g. y1 = b + mx (let x = 0 when year is 1970). 3. Sketch both functions on the same graph paper. 4. Solve for y when year is 1983 and 1998 (remember x = 0 in 1970) 5. Find the year when there is a difference between sales prices either graphically or solving equations y1 - y2 = difference or y2 = 2 y1 for
doubling problem.
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