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.

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