1. Adapt the bathtub model to medicine: First model the metabolization and elimination of medicine from the bloodstream (assume a 30% reduction of medicine per hour). Then add a constant inflow of 1 gram/minute of medicine to the bloodstream through an IV drip. If the therapeutic level of the medicine is between 150 grams and 275 grams, how many minutes does it take to reach the therapeutic level? [Run for 2000 minutes.] Repeat with shots that administer 125 grams each time they are given. How often do the shots need to be administered for the medicine in the bloodstream to enter and remain within the therapeutic region? How long before the medicine in the bloodstream consistently stays in the therapeutic region? [Hint: Use the PULSE function to simulate shots given regularly. It will help you to create and graph two converters, one for the lower level and one for the upper level, against the level of medicine in the bloodstream.] 
2. (25 pts) Build the pension model. What behaviors can be generated from the pension model and under which conditions? Why is the behavior occurring? Keep the rate of return constant for these tests (changing it generates the same behaviors). 
3. (25 pts) You own and operate 17 oil wells. On average, you pump 242 barrels per day from each well (the reality varies dramatically from this average). What is your total oil production (by day) across one month? [Build a model.] 
4. (25 pts) Your friend has built a model (described below), but it doesn’t quite work. Use the description below to fix the model. Newton’s law of cooling says that the rate of change of temperature of an object is directly proportional to the difference between the object’s temperature and the temperature surrounding it (the ambient temperature). When the object is warmer than the ambient temperature, this leads to an exponential decay toward the ambient temperature (this is how time of death is normally fixed). It works even when the object is colder than the ambient temperature, in which case the object approaches the ambient temperature asymptotically from below (this is just the exponential decay flipped vertically). The proportionality constant varies with the object; use 0.05 for this exercise. Use 70 degrees as the ambient temperature. Your friend’s model has a stock called Temperature, representing the temperature of the object, initialized to 120 with an outflow called lowering equal to 10. Will this create the correct behavior? Why not? What’s missing and what’s not formulated correctly? Fix the model and show the correct behavior. Does your revised model properly handle the case where the object’s temperature is below the ambient temperature? Set the stock Temperature to 35 and run the model again. Did the object warm to the ambient temperature? Why or why not? Change your model so this case also works.