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.

At t = 0 there are 2.2 million worms and 1 thousand robins.
(a) Use the differential equations to calculate the derivatives dw∕dt and dr∕dt at t = 0.
(b) Use the initial values and your answer to part (a) to estimate the number of robins and worms at t = 0.1.
(c) Using the method of part (a) and (b), estimate the number of robins and worms at t = 0.2 and 0.3.

Transcribed Image Text:

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)