Question 23.89

59. (Requires programmable calculator, spreadsheet, or BASIC programming) A population model slightly different from the logistic model is given by the iterative function system

985

where is a fraction of the limiting population and is a growth rate.

  1. Set , start with , and calculate the first 20 values .
  2. In part (a), you should have found . Replace this value with the rounded-up value and continue on to calculate .
  3. Now replace with the rounded-down value and continue on to calculate .

59.

(a) 0.0397, 0.15407173, 0.545072626, 1.288978, 0.171519142, 0.59782012, 1.31911379, 0.0562715776, 0.215586839, 0.722914301, 1.32384194, 0.0376952973, 0.146518383, 0.521670621, 1.27026177, 0.240352173, 0.78810119, 1.2890943, 0.171084847, 0.596529312

(b) 0.723, 1.323813, 0.0378094231, 0.146949035, 0.523014083, 1.27142514, 0.236134903, 0.777260536, 1.29664032, 0.142732915, 0.509813606

(c) 0.722, 1.324148, 0.0364882223, 0.141958718, 0.507378039, 1.25721473, 0.287092278, 0.901103183, 1.16845189, 0.577968093