The median size of a new single-family house built in the United States between 1987 and 2001 can be modeled by the equationH(x) = 0.359x3 - 15.198x2 + 221.738x + 862.514 square feetwhere x is the number of years after 1980. t(a) Determine the value of x in the domain 7sxS 21 for which the median house size was increasing least rapidly. (Round your answer to three decimal places.)Thus, in which year was the median house size was increasing least rapidly?Find the corresponding house size. (Round your answer to one decimal place.)square ftFind the corresponding rate of change in house size. (Round your answer to three decimal places.)square feet per year(b) Graph H.square footage1600-square footage18001600140014001200120010008001000600800400200600Years since 1980Years since 1980410 1214 16 18 20410 12 14 16 18 20

Answered: Image /qna-images/answer/f0b1955f-ce7a-4cfa-aa5f-3f6879e11b4e.jpg

Answered: The median size of a new single-family…

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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You purchased a car for $30 000. It depreciates by 25% of its current value every year. a) Write a function that can be used to model the value of the car after x years. b) How much will the car be worth 3 years after it is purchased? c) How long would it take for the car to depreciate to a value of $20 000?
The height of Jocelyn's rocket, in feet, as a function of time, in seconds, is modeled by the equation J(t)=-16t^2+180t. The height of Kelly's rocket, in feet, as a function of time, in seconds, is modeled by the equation K(t)=-16t^2+240t. a. Evealuate J(3) b. Who would win a rocket launching contest by having the highest flying rocket? c. How much more time did it take for the second rocket to hit the ground? d. If we launch Kelly's rocket from a height of 12 feet how does that change Kelly's function K(t)?
Suppose the profit P (in dollars) of a certain item is given by P = 1.25x − 650, where x is the number of items sold. Graph this profit relationship.
In 2000, the value of a home is 150,000.00 dollars. Its value has been increasing 5% per year. If this rate continues indefinitely, write an equation, in function notation, to represent the value of the home as a function of time, t, in years since 2000
In which year are PEV sales projected to equal 8.2 %of total vehicle sales?
The percent of high school students who smoked cigarettes on 1 or more of the 30 days preceding the survey is given by y = -0.064x² +0.277x +33.715, where x is the number of years after 1990. During what years from 1990 on is the percent greater than 30%? From to the percent is greater than 30%. (Round up to the nearest year as needed.)
The closing stock price of a company for the years 2009 to 2023 was approximated using the function f(x) = - 0. 32x2 + 12x - 48, where X = 9 corresponds to the start of the year 2009. What was the company's stock price at the start of 2023?

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