Assignment 4 – Loops and More Discrete Time Systems Due Date: September 20, 2011 1. Include your script Lab3Loops.R (just copy and paste). How much medication is in the body after 47 time steps with a dose of 500mg? 2. Write a script to compute the following sum. Hint: this script will use the index values inside the for loop. Include your script in your report (just copy and paste). What is the sum when m = 5? m = 14? m = 250? BONUS: What does this series coverge to? In other words, if we let m get really, really big what does this add to? Hint: I don’t just want the value R gives you if you make m big. The answer involves a very famous irrational number. 3. Write a script to simulate the following discrete time dynamical system for the lung model you discussed during lecture (section 1.9). Suppose the equilibrium value of this system is 10mmol/L. If , meaning that air is being exchanged, what should be to get this equilibrium value? Using this value of , simulate the system using your script for different values of q. How do different values of q change the system? Be specific.