Let w be the number of worms (in millions) and r the number of robins (in thousands) living on an island. Suppose w and r satisfy the following differential equations, which correspond to the slope field in Figure 9.44.

(a) Assume that there are 3 million worms and 2 thousand robins. Locate the point corresponding to this situation on the slope field given in Figure 9.44. Draw the trajectory through this point.
(b) In which direction does the point move along this trajectory? Put an arrow on the trajectory and justify your answer using the differential equations for dr∕dt and dw∕dt given in this section.
(c) How large does the robin population get? What is the size of the worm population when the robin population is at its largest?
(d) How large does the worm population get? What is the size of the robin population when the worm population is at its largest?

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3 dw dt r (predator) 4 = w-wr, 1 11/ 117 11/ 1/ 1 1/2 1/// 21/ 117 117 17 | |/\| dr dt V 1 1 1 1 1 1 1 1 1 || = -r+wr. / / / / / / / / / / / 1 ///// 1 2 Figure 9.44: dr. dw 3 r(W-1) w(1-r) w (prey)