Assignment 3 – Scripts and Discrete Time Dynamical Systems Due Date: September 13, 2011 1. Write a script to simulate the following discrete time dynamical system. One interpretation for this system is thinking of B as the number of bacteria in your body . In each time step half of the bacteria reproduce. However, due to treatment, h bacteria are killed in each time step. 2. Let h be 100. Simulate the system for and for 15 time steps. What happens for both cases and why does there seem to be a problem with the model when ? In this case, what is the equilibrium value? 3. Simulate this dynamical system two more times with different values of h and . Record your final values, number of time steps, what the system appears to be doing, and the equilibrium values. BONUS: Write a line of code in your script that solves for the equilibrium value of the system for any value of h. Include this line of code in your report for an extra point. Report Answer the questions in bold from Lab 3. Complete the assignment above and be sure to include answers to all questions and all the results from your simulations. Think through your answers very carefully. Make sure they are clear and complete. Note: You do not need to include your actual scripts in this report.