Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Sent to:
Search glass icon
  • Login
  • Textbooks
  • Ask our Educators
  • Study Tools
    Study Groups Bootcamps Quizzes AI Tutor iOS Student App Android Student App StudyParty
  • For Educators
    Become an educator Educator app for iPad Our educators
  • For Schools

Problem

In Examples 1 we used Lotka-Volterra equations to…

12:18

Question

Answered step-by-step

Problem 10 Easy Difficulty

Populations of aphids and ladybugs are modeled by the equations
$ \frac {dA}{dt} = 2A - 0.01AL $
$ \frac {dL}{dt} =0.5L + 0.0001AL $
(a) Find the equilibrium solutions and explain their significance.
(b) Find an expression for $ dL/dA. $
(c) The direction field for the differential equation in part (b) is shown. Use it to sketch a phase portrait. What do the phase trajectories have in common?
(d) Suppose that at time $ t = 0 $ there are 1000 aphids and 200 ladybugs. Draw the corresponding phase trajectory and use it to describe how both populations change.
(e) Use part (d) to make rough sketches of the aphid and ladybug populations as function of $ t. $ How are the graphs related to each other?


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

Lainey Roebuck
Numerade Educator

Like

Report

Textbook Answer

Official textbook answer

Video by Lainey Roebuck

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Related Courses

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 9

Differential Equations

Section 6

Predator-Prey Systems

Related Topics

Differential Equations

Discussion

You must be signed in to discuss.
Top Calculus 2 / BC Educators
Anna Marie Vagnozzi

Campbell University

Kayleah Tsai

Harvey Mudd College

Kristen Karbon

University of Michigan - Ann Arbor

Michael Jacobsen

Idaho State University

Calculus 2 / BC Courses

Lectures

Video Thumbnail

13:37

Differential Equations - Overview

A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders. An ordinary differential equation (ODE) is a differential equation containing one or more derivatives of a function and their rates of change with respect to the function itself; it can be used to model a wide variety of phenomena. Differential equations can be used to describe many phenomena in physics, including sound, heat, electrostatics, electrodynamics, fluid dynamics, elasticity, quantum mechanics, and general relativity.

Video Thumbnail

33:32

Differential Equations - Example 1

A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders. An ordinary differential equation (ODE) is a differential equation containing one or more derivatives of a function and their rates of change with respect to the function itself; it can be used to model a wide variety of phenomena. Differential equations can be used to describe many phenomena in physics, including sound, heat, electrostatics, electrodynamics, fluid dynamics, elasticity, quantum mechanics, and general relativity.

Join Course
Recommended Videos

0:00

Populations of aphids and …

01:31

Populations of aphids and …

03:05

Aphid-ladybug dynamics Pop…

07:48

In Exercise 10 we modeled …

02:35

Modified aphid-ladybug dyn…

0:00

In Exercise 10 we modeled …

Watch More Solved Questions in Chapter 9

Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12

Video Transcript

So if a and l are constant than a prime and l prime equals 0, so we have 0 equals 2, a minus 0.01, a l, and then we have 0 equals negative 0.5 l plus 0.0001, a l and that goes to 0 equals a times. 2. Minus 0.01 l and 0 equals l times negative 0.5 plus 0.001, a for part b. We have d l over d, a is equal to d l d, t over d, a d t and that is negative: 0.5 l plus 0.0001, a l divided by 2, a minus 0.01, a l for part c. The solution curves are all closed. Curves that have the equilibrium .5200 inside them. For part d, we have at p not 1 thousamdand, 200 d. A d t is equal to 0 and d. L over dt is equal to negative 80, which is less than 0, so the number of lady bugs is decreasing and is going and the counter clockwise direction and at p 1 equals 5100. The lady bug population increases dramatically with a maximum of p 21425200 point. So for part e, both graphs have the same period and the graph of l peaks about a quarter of a cycle after the graph of a to kind of show you that here's the graph over here is a over here is l. We have 30000 point, and then here over here we have 900 and then 100 okay. So we have a and l and if we start with l, l starts about below 10000 decreases. First goes up to about 15000 decreases again, and then it reaches this axis. At 200 and then for a a increases first below 5000 peaks at about 15000, just like l goes down and drops very low, then goes all the way back up peaks just right before l does and it ends way below 100 point.

Get More Help with this Textbook
James Stewart

Calculus: Early Transcendentals

View More Answers From This Book

Find Another Textbook

Study Groups
Study with other students and unlock Numerade solutions for free.
Math (Geometry, Algebra I and II) with Nancy
Arrow icon
Participants icon
129
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
63
Hosted by: Alonso M
See More

Related Topics

Differential Equations

Top Calculus 2 / BC Educators
Anna Marie Vagnozzi

Campbell University

Kayleah Tsai

Harvey Mudd College

Kristen Karbon

University of Michigan - Ann Arbor

Michael Jacobsen

Idaho State University

Calculus 2 / BC Courses

Lectures

Video Thumbnail

13:37

Differential Equations - Overview

A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders. An ordinary differential equation (ODE) is a differential equation containing one or more derivatives of a function and their rates of change with respect to the function itself; it can be used to model a wide variety of phenomena. Differential equations can be used to describe many phenomena in physics, including sound, heat, electrostatics, electrodynamics, fluid dynamics, elasticity, quantum mechanics, and general relativity.

Video Thumbnail

33:32

Differential Equations - Example 1

A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders. An ordinary differential equation (ODE) is a differential equation containing one or more derivatives of a function and their rates of change with respect to the function itself; it can be used to model a wide variety of phenomena. Differential equations can be used to describe many phenomena in physics, including sound, heat, electrostatics, electrodynamics, fluid dynamics, elasticity, quantum mechanics, and general relativity.

Join Course
Recommended Videos

0:00

Populations of aphids and ladybugs are modeled by the equations $$ \begin{array…

01:31

Populations of aphids and ladybugs are modeled by the equations $$ \begin{al…

03:05

Aphid-ladybug dynamics Populations of aphids and ladybugs are modeled by the eq…

07:48

In Exercise 10 we modeled populations of aphids and ladybugs with a Lotka-Volte…

02:35

Modified aphid-ladybug dynamics In Exercise 22 we modeled populations of aphids…

0:00

In Exercise 10 we modeled populations of aphids and ladybugs with a Lotka-Volte…
Additional Mathematics Questions

01:22

A computer costs $520 in the United States. The same model costs 525 euros i…

01:11

Explain how poor communication can affect the smooth running of an organisat…

02:05

For a bond issue that sells for more than the bond face amount, the stated i…

01:18

Find the measure of angle x. Round your answer to the nearest hundredth. (pl…

01:36

fold a 3 inch by 5 inch index card on one of its diagonals

02:54

Find the coordinates of the point 7/10 of the way on a segment from A(3, -4)…

01:09

Which of the following steps is included in the construction of a parallel l…

00:55

If r and s are parallel lines, and the measure of a is 146 degrees, what is …

02:25

Find an equation for the perpendicular bisector of the line segment whose en…

02:41

The Wilson family's back yard is a rectangular plot that has a length o…

Add To Playlist

Hmmm, doesn't seem like you have any playlists. Please add your first playlist.

Create a New Playlist

`

Share Question

Copy Link

OR

Enter Friends' Emails

Report Question

Get 24/7 study help with our app

 

Available on iOS and Android

About
  • Our Story
  • Careers
  • Our Educators
  • Numerade Blog
Browse
  • Bootcamps
  • Books
  • Notes & Exams NEW
  • Topics
  • Test Prep
  • Ask Directory
  • Online Tutors
  • Tutors Near Me
Support
  • Help
  • Privacy Policy
  • Terms of Service
Get started