Question

In 1990 the U.S. population, broken down by regions, was $50.8$ million in the Northeast, $59.7$ million in the Midwest, $85.4$ million in the South, and $52.8$ million in the West. ${ }^{4}$ Between 1990 and 2000, the population in the Northeast grew by $2.8$ million, the population in the Midwest grew by $4.7$ million, the population in the South grew by $14.8$ million, and the population in the West grew by $10.4$ million. Set up the population figures for 1990 and the growth figures for the decade as row vectors. Assuming that the population will grow by the same numbers from 2000 to 2010 as they did from 1990 to 2000 , show how to use matrix operations to find the population in each region in 2010 . 

          In 1990 the U.S. population, broken down by regions, was $50.8$ million in the Northeast, $59.7$ million in the Midwest, $85.4$ million in the South, and $52.8$ million in the West. ${ }^{4}$ Between 1990 and 2000, the population in the Northeast grew by $2.8$ million, the population in the Midwest grew by $4.7$ million, the population in the South grew by $14.8$ million, and the population in the West grew by $10.4$ million. Set up the population figures for 1990 and the growth figures for the decade as row vectors. Assuming that the population will grow by the same numbers from 2000 to 2010 as they did from 1990 to 2000 , show how to use matrix operations to find the population in each region in 2010 .
Show more…

Added by Stacie T.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
AceChat toggle button
Close icon
Ace pointing down

Please give Ace some feedback

Your feedback will help us improve your experience

Thumb up icon Thumb down icon
Thanks for your feedback!
Profile picture
In 1990 the U.S. population, broken down by regions, was $50.8$ million in the Northeast, $59.7$ million in the Midwest, $85.4$ million in the South, and $52.8$ million in the West. Between 1990 and 2000, the population in the Northeast grew by $2.8$ million, the population in the Midwest grew by $4.7$ million, the population in the South grew by $14.8$ million, and the population in the West grew by $10.4$ million. Set up the population figures for 1990 and the growth figures for the decade as row vectors. Assuming that the population will grow by the same numbers from 2000 to 2010 as they did from 1990 to 2000 , show how to use matrix operations to find the population in each region in 2010 .
Close icon
Play audio
Feedback
Powered by NumerAI
Ivan Kochetkov David Collins
Jennifer Stoner verified

Brian Beasley and 86 other subject Calculus 1 / AB educators are ready to help you.

Ask a new question
*

Labs

-

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs
*

Key Concepts

-
Key Concept
Premium Feature
Explore the core concept behind this problem.
Play button
Key Concept
Premium Feature
Explore the core concept behind this problem.
Your browser does not support the video tag.
*

Recommended Videos

-
population-movement-in-2000-country-population-broken-down-by-regions-was-536-million-in-the-northeast-644-million-the-midwest-100_-million-the-south-and-632-million-the-west-in-2010-the-pop-66987

Population Movement In 2000 a country's population, broken down by regions, was 53.6 million in the Northeast, 64.4 million in the Midwest, 100.2 million in the South, and 63.2 million in the West. In 2010 the population was 61.3 million in the Northeast, 73.9 million in the Midwest, 115.6 million in the South, and 64.9 million in the West. Set up the population figures for each year as a row vector. Northeast Midwest South West Population in 2000 (in millions) Population in 2010 (in millions) Use matrix operations to find the net increase or decrease of population in each region from 2000 to 2010. Northeast Midwest South West Population Net Change (in millions) Assuming the same population growth from 2010 to 2020 as from 2000 to 2010, use matrix operations to predict the population in each region in 2020. Northeast Midwest South West Population in 2020 (in millions)

Sri K.
population-movement-in-2000-a-countrys-population-broken-down-by-regions-was-536-million-in-the-northeast-644-million-in-the-midwest-1002-million-in-the-south-and-632-million-in-the-west-in-2010-the-p

Population Movement In 2000 a country's population, broken down by regions, was 53.6 million in the Northeast, 64.4 million in the Midwest, 100.2 million in the South, and 63.2 million in the West. In 2010 the population was 56.3 million in the Northeast, 67.9 million in the Midwest, 116.6 million in the South, and 66.9 million in the West. Set up the population figures for each year as a row vector. Northeast Midwest South West Population in 2000 (in millions) Population in 2010 (in millions) Use matrix operations to find the net increase or decrease of population in each region from 2000 to 2010. Northeast Midwest South West Population Net Change (in millions) Assuming the same population growth from 2010 to 2020 as from 2000 to 2010, use matrix operations to predict the population in each region in 2020. Northeast Midwest South West Population in 2020 (in millions)

William S.
the-population-in-millions-of-the-united-states-between-1970-and-2010-can-be-modeled-as-px-20312e0011x-million-people-where-x-is-the-number-of-decades-after-1970-the-percentage-of-people-in-95046

The population (in millions) of the United States between 1970 and 2010 can be modeled as: p(x) = 203.12e^(0.011x) million people where x is the number of decades after 1970. The percentage of people in the United States who live in the Midwest between 1970 and 2010 can be modeled as: m(x) = 0.002x^2 - 0.213x + 27.84 percent where x is the number of decades since 1970. (a) Write an expression for the number of people who live in the Midwest x decades after 1970. f(x) = 203.12e^(0.011x)(0.002x^2 - 0.213x + 27.84) * 100 million people (b) Write an expression for the rate of change of the population of the Midwest. f'(x) = 203.12e^(0.011x)(0.004x - 0.213) million people per decade (c) How rapidly was the population of the Midwest changing in 2000 and in 2010? (Round your answers to three decimal places.) 2000: 0.011 * 2000 = 22 f'(22) = 203.12e^(0.011 * 22)(0.004 * 22 - 0.213) million people per decade 2010: 0.011 * 2010 = 22.11 f'(22.11) = 203.12e^(0.011 * 22.11)(0.004 * 22.11 - 0.213) million people per decade

Vaidik S.
*

Recommended Textbooks

-
Calculus: Early Transcendentals

Calculus: Early Transcendentals

James Stewart 8th Edition
achievement 1,445 solutions
Calculus: Early Transcendentals

Calculus: Early Transcendentals

William Briggs, Lyle Cochran, Bernard Gillet 3rd Edition
achievement 1,685 solutions
Thomas Calculus

Thomas Calculus

George B. Thomas Jr. 14th Edition
achievement 1,711 solutions
*

Transcript

-
00:01 In this problem, we're given the population figures in millions for the united states in 1990 by regions.
00:07 We're also told the growth in the population in millions over the decade from 1990 to 2000.
00:14 Our job is, assuming that the growth was the same from 2000 to 2010, what will the population be in 2010? so to set this problem up, we're using row matrices.
00:29 We have written the population.
00:31 By region in 1990 in the following one by four matrix, where you can think of the columns of standing for northeast, midwest, south, and west, respectively.
00:42 And now we're going to have a second matrix.
00:44 That's matrix a, matrix b.
00:46 We'll represent the growth in the population in each region from 1990 to 2000.
00:51 So those figures and millions are also given in the problem.
00:55 So let's fill those in.
00:57 So here's matrix b, also a one by four matrix.
01:06 And now we don't have to write.
01:08 What each column represents each time, but this first time through we'll do that.
01:14 Now, we want to find the population in 2010, and we're assuming that the same growth represented by matrix b occurs again.
01:22 So the matrix we want to calculate is a plus 2b.
01:28 All right.
01:29 So we have matrix a, which we will just copy over, and then we need to add twice b.
01:42 So we'll come down here and multiply each entry in b by 2.
01:47 That produces this new matrix.
01:51 And i need to go back up and take out those plus signs...
Need help? Use Ace
Ace is your personal tutor. It breaks down any question with clear steps so you can learn.
Start Using Ace
Ace is your personal tutor for learning
Step-by-step explanations
Instant summaries
Summarize YouTube videos
Understand textbook images or PDFs
Study tools like quizzes and flashcards
Listen to your notes as a podcast
Continue solving this problem
Create a free account to:
  • View full step-by-step solution
  • Ask follow-up questions with Ace AI
  • Save progress and study later
Continue Free
Join the community

18,000,000+

Students on Numerade

Trusted by students at 8,000+ universities

Numerade

Get step-by-step video solution
from top educators

Continue with Clever
or



By creating an account, you agree to the Terms of Service and Privacy Policy
Already have an account? Log In

A free answer
just for you

Watch the video solution with this free unlock.

Numerade

Log in to watch this video
...and 100,000,000 more!


EMAIL

PASSWORD

OR
Continue with Clever