The purchase price of a home y (in $1000) can be approximated based on the annual income of the buyer x1 (in $1000) and on the square footage of the home x2 (in 100 ft2) according to y = ax1 + bx2 + c. The table gives the incomes of three buyers, the square footages of the home purchased, and the corresponding purchase prices of the home. Square Footage (100 ft’) x2 Income Price ($1000) x1 ($1000) y 80 21 180 150 28 250 75 18 160 a. Use the data to write a system of linear equations to solve for a, b, and c. b. Use a graphing utility to find the reduced row-echelon form of the augmented matrix. c. Write the model y = ax1 + bx2 + c. d. Predict the purchase price for a buyer who makes $100,000 per year and wants a 2500 ft2 home.
The purchase price of a home y (in $1000) can be approximated based on the annual income of the buyer x1 (in $1000) and on the square footage of the home x2 (in 100 ft2) according to y = ax1 + bx2 + c. The table gives the incomes of three buyers, the square footages of the home purchased, and the corresponding purchase prices of the home. Square Footage (100 ft’) x2 Income Price ($1000) x1 ($1000) y 80 21 180 150 28 250 75 18 160 a. Use the data to write a system of linear equations to solve for a, b, and c. b. Use a graphing utility to find the reduced row-echelon form of the augmented matrix. c. Write the model y = ax1 + bx2 + c. d. Predict the purchase price for a buyer who makes $100,000 per year and wants a 2500 ft2 home.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:The purchase price of a home y (in $1000) can be approximated based on the annual income of the buyer x1 (in $1000)
and on the square footage of the home x2 (in 100 ft2) according to y = ax1 + bx2 + c.
The table gives the incomes of three buyers, the square footages of the home purchased, and the corresponding purchase
prices of the home.
Square Footage
(100 ft’) x2
Income
Price
($1000) x1
($1000) y
80
21
180
150
28
250
75
18
160
a. Use the data to write a system of linear equations to solve for a, b, and c.
b. Use a graphing utility to find the reduced row-echelon form of the augmented matrix.
c. Write the model y = ax1 + bx2 + c.
d. Predict the purchase price for a buyer who makes $100,000 per year and wants a 2500 ft2 home.
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