Problem #7: The updating function for the discrete time dynamical system $m_{t+1} = f(m_t)$ is given in the figure below.
In each part below, start from the given initial condition and determine the sequence of points which form the
correct cobwebbing diagram when the points are connected.
(a) $m_0 = 5.5$.
(b) $m_0 = 4.5$.
(A) (5.5, 5), (5,5), (5, 4.75), (4.75, 4.75), (4.75, 4.625), (4.625,4.625)
(B) (5.5, 4.5), (4.5, 4.5), (4.5, 4), (4, 4), (4, 3.75), (3.75,3.75)
(C) (5.5, 6.5), (6.5, 6.5), (6.5, 7), (7,7), (7,7.25), (7.25,7.25)
(D) (5.5, 5), (5, 5), (5, 4.25), (4.25, 4.25), (4.25, 3.125), (3.125, 3.125)
(E) (5.5, 7), (7,7), (7,7.75), (7.75,7.75), (7.75,8.125), (8.125,8.125)
(F) (5.5, 6), (6,6), (6, 6.75), (6.75, 6.75), (6.75, 7.875), (7.875,7.875) (G) (5.5,6), (6,6), (6, 7), (7,7), (7,9), (9,9)
(H) (5.5, 5), (5,5), (5, 4), (4, 4), (4, 2), (2, 2)
Problem #7(a): Select ☑ ↑ Part (a) choices.
(A) (4.5, 6), (6,6), (6, 6.75), (6.75, 6.75), (6.75, 7.125), (7.125, 7.125)
(B) (4.5, 5), (5, 5), (5,5.75), (5.75,5.75), (5.75, 6.875), (6.875,6.875) (C) (4.5, 4), (4, 4), (4, 3), (3, 3), (3, 1), (1, 1)
(D) (4.5, 5.5), (5.5,5.5), (5.5, 6), (6, 6), (6, 6.25), (6.25,6.25) (E) (4.5, 5), (5, 5), (5,6), (6,6), (6,8), (8,8)
(F) (4.5, 4), (4, 4), (4, 3.75), (3.75, 3.75), (3.75, 3.625), (3.625,3.625)
(G) (4.5, 4), (4, 4), (4, 3.25), (3.25, 3.25), (3.25, 2.125), (2.125, 2.125)
(H) (4.5,3.5), (3.5,3.5), (3.5, 3), (3, 3), (3, 2.75), (2.75, 2.75)
Problem #7(b): Select ☑ ↑ Part (b) choices.
