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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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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.
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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