EBK DIFFERENTIAL EQUATIONS
5th Edition
ISBN: 9780100802452
Author: Calvis
Publisher: YUZU
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 4.2, Problem 17P
Program Plan Intro
Program Description: Purpose of problem is to obtain the general solution of the linear system of the differential equation
Expert Solution & Answer
![Check Mark](/static/check-mark.png)
Want to see the full answer?
Check out a sample textbook solution![Blurred answer](/static/blurred-answer.jpg)
Students have asked these similar questions
Chapter 13, Section 13.1, Problem 018
Bob's Pest Removal Service specializes in removing wild creatures (skunks, bats, reptiles, etc.) from private homes. He charges $69 to go to a house plus $25 per hour for his services. Let y be the
total amount (in dollars) paid by a household using Bob's services and x the number of hours Bob spends capturing and removing the animal(s). The equation for the relationship between x and y is
y = 25x + 69.
a. Bob spent 3 hours removing a coyote from under Alice's house. How much will he be paid?
Bob will be paid $
exact number, no tolerance
b. Suppose nine persons called Bob for assistance during a week. Strangely enough, each of these jobs required exactly 3 hours. Will each of these clients pay Bob the same amount, or do you
expect each one to pay a different amount?
Each of the clients will pay Bob the same amount.
Each of the clients will pay Bob a different amount.
c. Is the relationship between x and y exact or nonexact?
Version 4.24.20.1…
1. Suppose that at some initial point in time 100,000 people live in Auckland city and 25,000 people live in
its suburbs. After conducting a research, the Regional Planning Commission determines that the model
governing people's movement between Auckland and its suburbs is given by the equations:
an+1 = 0.95a, + 0.03s
Sn+1 = 0.05a, +0.97sn
where an, is the number of people in Auckland and s, is the number of people in the suburbs.
(a) Using column vectors, write the transition matrix A.
(b) Assuming that the total population remains constant, by using Xn+1 = Ax, to compute the first five
state vectors, find the population of Auckland city and its suburbs over a period of five years.
(e) Write x₁, as a linear combination of the eigenvectors of A and use it to predict the first five state
vectors. Confirm that your answers are the same as in Question (1b).
(d) What does the model predict in the long term.
Note: we have used Xn to denote the vector
an
8p
Problem 1:
In the Lotka-Volterra predator-prey model, the number of foxes and rabbits in a park depend on
each other. When there are many rabbits, the population of foxes increases but when there are
many foxes, the population of rabbits decreases. The following equation provides the Lotka-Volterra
model for the number of foxes, F, and the number of rabbits, R, in Eagle Park.
21.4 = -0.002R+0.4 ln(R) – 0.01F + 4 ln(F).
A graph showing the curve given by this equation is given below.
dF
(a) Find a formula for
dR
Foxes
(b) Based on the graph, what do you expect the
dF
to be when the number of foxes
dR
value of
500
in the park is at its highest or lowest value?
dF
and your answer
dR
400
(c) Using your formula for
to part (b), determine the number of rabbits
in the park when the fox population is at its
highest or lowest value.
300
200
(d) Using the model and your answer to part (c),
100
determine the maximum and minimum val-
ues for the size of the fox population in Eagle
Park. You will…
Chapter 4 Solutions
EBK DIFFERENTIAL EQUATIONS
Ch. 4.1 - Prob. 1PCh. 4.1 - Prob. 2PCh. 4.1 - Prob. 3PCh. 4.1 - Prob. 4PCh. 4.1 - Prob. 5PCh. 4.1 - Prob. 6PCh. 4.1 - Prob. 7PCh. 4.1 - Prob. 8PCh. 4.1 - Prob. 9PCh. 4.1 - Prob. 10P
Ch. 4.1 - Prob. 11PCh. 4.1 - Prob. 12PCh. 4.1 - Prob. 13PCh. 4.1 - Prob. 14PCh. 4.1 - Prob. 15PCh. 4.1 - Prob. 16PCh. 4.1 - Prob. 17PCh. 4.1 - Prob. 18PCh. 4.1 - Prob. 19PCh. 4.1 - Prob. 20PCh. 4.1 - Prob. 21PCh. 4.1 - Prob. 22PCh. 4.1 - Prob. 23PCh. 4.1 - Prob. 24PCh. 4.1 - Prob. 25PCh. 4.1 - Prob. 26PCh. 4.1 - Prob. 27PCh. 4.1 - Prob. 28PCh. 4.1 - Prob. 29PCh. 4.1 - Prob. 30PCh. 4.1 - Prob. 31PCh. 4.1 - Prob. 32PCh. 4.1 - Prob. 33PCh. 4.1 - Repeat Problem 33, except with the generator...Ch. 4.1 - A particle of mass m moves in the plane with...Ch. 4.1 - Prob. 36PCh. 4.1 - Prob. 37PCh. 4.2 - Prob. 1PCh. 4.2 - Prob. 2PCh. 4.2 - Prob. 3PCh. 4.2 - Prob. 4PCh. 4.2 - Prob. 5PCh. 4.2 - Prob. 6PCh. 4.2 - Prob. 7PCh. 4.2 - Prob. 8PCh. 4.2 - Prob. 9PCh. 4.2 - Prob. 10PCh. 4.2 - Prob. 11PCh. 4.2 - Prob. 12PCh. 4.2 - Prob. 13PCh. 4.2 - Prob. 14PCh. 4.2 - Prob. 15PCh. 4.2 - Prob. 16PCh. 4.2 - Prob. 17PCh. 4.2 - Prob. 18PCh. 4.2 - Prob. 19PCh. 4.2 - Prob. 20PCh. 4.2 - Suppose that L1=a1D2+b1D+c1 and L2=a2D2+b2D+c2,...Ch. 4.2 - Suppose that L1x=tDx+x and that L2x=Dx+tx. Show...Ch. 4.2 - Prob. 23PCh. 4.2 - Prob. 24PCh. 4.2 - Prob. 25PCh. 4.2 - Prob. 26PCh. 4.2 - Prob. 27PCh. 4.2 - Prob. 28PCh. 4.2 - Prob. 29PCh. 4.2 - Prob. 30PCh. 4.2 - Prob. 31PCh. 4.2 - Prob. 32PCh. 4.2 - Prob. 33PCh. 4.2 - Prob. 34PCh. 4.2 - Prob. 35PCh. 4.2 - Prob. 36PCh. 4.2 - Prob. 37PCh. 4.2 - Prob. 38PCh. 4.2 - Prob. 39PCh. 4.2 - Prob. 40PCh. 4.2 - Prob. 41PCh. 4.2 - Prob. 42PCh. 4.2 - Prob. 43PCh. 4.2 - Prob. 44PCh. 4.2 - Prob. 45PCh. 4.2 - Prob. 46PCh. 4.2 - Prob. 47PCh. 4.2 - Prob. 48PCh. 4.3 - Prob. 1PCh. 4.3 - Prob. 2PCh. 4.3 - Prob. 3PCh. 4.3 - Prob. 4PCh. 4.3 - Prob. 5PCh. 4.3 - Prob. 6PCh. 4.3 - Prob. 7PCh. 4.3 - Prob. 8PCh. 4.3 - Prob. 9PCh. 4.3 - Prob. 10PCh. 4.3 - Prob. 11PCh. 4.3 - Prob. 12PCh. 4.3 - Prob. 13PCh. 4.3 - Prob. 14PCh. 4.3 - Suppose that a projectile is fired straight upward...Ch. 4.3 - Prob. 16PCh. 4.3 - Prob. 17PCh. 4.3 - Prob. 18PCh. 4.3 - Prob. 19PCh. 4.3 - Prob. 20PCh. 4.3 - Suppose that an artillery projectile is fired from...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Similar questions
- Imagine that as a ball is tossed, its motion is tracked on a coordinate plane. Given only a few of the points that the ball passes through, it is actually possible to determine the equation of the parabola that represents the ball’s path through the air. Assume the ball passes through the points (3,8), (5,20/3), and (6,5). Use this data to set up a system of three equations and three unknowns (a, b, and c) that will allow you to find the equation of the parabola and assume that x represents the number of seconds that have passed since the ball was thrown: determine approximately how long it will take for the ball to hit the ground.arrow_forwardFind the general solution to the following 3-by-3 linear system: 1 -5 10 dx 2 -4 8. 8 x. dt 3 -5 8arrow_forwardRework problem 17 from section 5.1 of your text, involving the production of basketballs. Assume that the number of defective basketballs produced is related by a linear equation to the total number produced. Suppose that 6 defective balls are produced in a lot of 300, and 15 defective balls are produced in a lot of 425. Find the number of defective balls produced in a lot of 675 balls.arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningAlgebra for College StudentsAlgebraISBN:9781285195780Author:Jerome E. Kaufmann, Karen L. SchwittersPublisher:Cengage LearningAlgebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell
![Text book image](https://www.bartleby.com/isbn_cover_images/9781285463247/9781285463247_smallCoverImage.gif)
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
![Text book image](https://www.bartleby.com/isbn_cover_images/9781285195780/9781285195780_smallCoverImage.gif)
Algebra for College Students
Algebra
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Cengage Learning
![Text book image](https://www.bartleby.com/isbn_cover_images/9780395977224/9780395977224_smallCoverImage.gif)
Algebra: Structure And Method, Book 1
Algebra
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:McDougal Littell