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In Examples 1 we used Lotka-Volterra equations to model populations of rabbits and wolves. Let's modify those equations as follows: $ \frac {dR}{dt} = 0.08R(1 - 0.0002R) - 0.001RW $ $ \frac {dW}{dt} = -0.02W + 0.00002RW $ (a) According to these equations, what happens to the rabbit population in the absence of wolves? (b) Find all the equilibrium solutions and explain their significance. (c) The figure shows the phase trajectory that starts at the point (1000, 40). Describe what eventually happens to the rabbit and wolf populations. (d) Sketch graphs of the rabbit and wolf populations as function of time.

          In Examples 1 we used Lotka-Volterra equations to model populations of rabbits and wolves. Let's modify those equations as follows:
$ \frac {dR}{dt} = 0.08R(1 - 0.0002R) - 0.001RW $
$ \frac {dW}{dt} = -0.02W + 0.00002RW $
(a) According to these equations, what happens to the rabbit population in the absence of wolves?
(b) Find all the equilibrium solutions and explain their significance.
(c) The figure shows the phase trajectory that starts at the point (1000, 40). Describe what eventually happens to the rabbit and wolf populations.
(d) Sketch graphs of the rabbit and wolf populations as function of time.

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Added by Christopher H.

Calculus: Early Transcendentals

James Stewart 8th Edition

Chapter 9

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Solved by Expert Arjun Khokher

Step 1

So, we have: $$\frac{dR}{dt} = 0.08R(1 - 0.0002R)$$ This is a logistic growth model for the rabbit population. In the absence of wolves, the rabbit population will grow until it reaches its carrying capacity, which can be found by setting $\frac{dR}{dt} = Show more…

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In Examples 1 we used Lotka-Volterra equations to model populations of rabbits and wolves. Let's modify those equations as follows: $ \frac {dR}{dt} = 0.08R(1 - 0.0002R) - 0.001RW $ $ \frac {dW}{dt} = -0.02W + 0.00002RW $ (a) According to these equations, what happens to the rabbit population in the absence of wolves? (b) Find all the equilibrium solutions and explain their significance. (c) The figure shows the phase trajectory that starts at the point (1000, 40). Describe what eventually happens to the rabbit and wolf populations. (d) Sketch graphs of the rabbit and wolf populations as function of time.

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