Suppose r(t) and y(t) measure two different populations of interest. The following system of differential equations is called a "competition" model: dx dt = x(a − bx − cy) dy dt with a, b, c, d, e, f all positive constants. (a) If r(t) = 0, what does the system reduce to? What model of population growth that we have learned about dictates how y grows? = y(d-ey- fx) (b) If y(t) = 0, what does the system reduce to? What model of population growth that we have learned about dictates how x grows? (c) Explain why this model is called a "competition" model. (d) Describe a real-world scenario where two species might be in competition with each other.
Suppose r(t) and y(t) measure two different populations of interest. The following system of differential equations is called a "competition" model: dx dt = x(a − bx − cy) dy dt with a, b, c, d, e, f all positive constants. (a) If r(t) = 0, what does the system reduce to? What model of population growth that we have learned about dictates how y grows? = y(d-ey- fx) (b) If y(t) = 0, what does the system reduce to? What model of population growth that we have learned about dictates how x grows? (c) Explain why this model is called a "competition" model. (d) Describe a real-world scenario where two species might be in competition with each other.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Pls answer a b c and d.
![+ Q
CD Page view
A Read aloud
dx
dt
[T] Add text
x(a - bx - cy)
8. Suppose (t) and y(t) measure two different populations of interest. The following
system of differential equations is called a "competition" model:
Draw
= y(d-ey- fx)
Highlight
Erase
dy
dt
with a, b, c, d, e, f all positive constants.
(a) If x(t) = 0, what does the system reduce to? What model of population growth
that we have learned about dictates how y grows?
3
(b) If y(t) = 0, what does the system reduce to? What model of population growth
that we have learned about dictates how a grows?
(c) Explain why this model is called a "competition" model.
(d) Describe a real-world scenario where two species might be in competition with
each other.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7907f5c6-c0b6-4b0b-9f85-e27f4227f9e5%2Ff4b5d90c-1464-4a5b-833f-73402e39f33c%2Fdckjphu_processed.jpeg&w=3840&q=75)
Transcribed Image Text:+ Q
CD Page view
A Read aloud
dx
dt
[T] Add text
x(a - bx - cy)
8. Suppose (t) and y(t) measure two different populations of interest. The following
system of differential equations is called a "competition" model:
Draw
= y(d-ey- fx)
Highlight
Erase
dy
dt
with a, b, c, d, e, f all positive constants.
(a) If x(t) = 0, what does the system reduce to? What model of population growth
that we have learned about dictates how y grows?
3
(b) If y(t) = 0, what does the system reduce to? What model of population growth
that we have learned about dictates how a grows?
(c) Explain why this model is called a "competition" model.
(d) Describe a real-world scenario where two species might be in competition with
each other.
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