Consider the following system of equations that model the strange dynamics between the two populations of Planet Math: x(t) denotes the population of the mathvillagers and y(t) denotes the population of the biocitizens; t is in years. d = y³ −0.5x² dt dt = y²x³ + 2 Let S(t) = (xs(t), ys(t)) be the solution of the system that goes through the point (2, 0.5) at some time to. Which of the following is true? O Immediately after to, both populations increase. O Immediately after to, the population of mathvillagers to decrease and that of the biocitizens to increase. O Immediately after to, the population of biocitizens to decrease and that of the mathvillager to increase. O Immediately after to, both populations increase.
Consider the following system of equations that model the strange dynamics between the two populations of Planet Math: x(t) denotes the population of the mathvillagers and y(t) denotes the population of the biocitizens; t is in years. d = y³ −0.5x² dt dt = y²x³ + 2 Let S(t) = (xs(t), ys(t)) be the solution of the system that goes through the point (2, 0.5) at some time to. Which of the following is true? O Immediately after to, both populations increase. O Immediately after to, the population of mathvillagers to decrease and that of the biocitizens to increase. O Immediately after to, the population of biocitizens to decrease and that of the mathvillager to increase. O Immediately after to, both populations increase.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 17EQ
Related questions
Question
Should I take the dy/dx of both first or divide them first? Please explain the answer alongside the steps. Thank you!
Transcribed Image Text:Consider the following system of equations that model the strange dynamics between the two populations of
Planet Math: x(t) denotes the population of the mathvillagers and y(t) denotes the population of the biocitizens; t
is in years.
dt
dy
dt
=
= y³ −0.5x²
=y²x³ + 2
Let S(t) = (xs(t), ys (t)) be the solution of the system that goes through the point (2, 0.5) at some time to.
Which of the following is true?
-
O Immediately after to, both populations increase.
O Immediately after to, the population of mathvillagers to decrease and that of the biocitizens to increase.
O Immediately after to, the population of biocitizens to decrease and that of the mathvillager to increase.
O Immediately after to, both populations increase.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps
Recommended textbooks for you
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage