So far, we have built models to explore a new job opportunity, to evaluate the cost of building a new product, and to analyze cash flows in a business. In all of these models we've been using what mathematicians call linear functions. Models built using linear functions have limits. In this lecture, we'll explore those limits, and find out how alternative mathematical functions can address other problems that linear functions can't. Also, our models so far have incorporated variables that are fixed. They are known quantities. That makes our models deterministic. Other models can be built to address uncertainty in business scenarios. Let's take a look at what makes the models we've worked with so far deterministic. Let's assume that we have worked with the sales forecast and cash flow model over the course of a full year. Now we have actuals in each period that we can use to compare to our forecast. They're here in row 19. I also added rows to show cumulative sales for the year. From the prior year, from current actuals, and the forecast. To generate a cumulative number, I added the cumulative number from the prior period to the current period sales. For example in cell D20, I added the value of C20, which was January's total to the period sales for February in D17. Let me graph these two cumulative sales numbers. The prior years sales and the projected sales. So in other words, the ranges from C20 through N21. I'll choose to insert a simple two dimensional line graph. Notice how the two cumulative lines run parallel with this years cumulative numbers ending somewhat higher. This is exactly what we would expect since we programmed the model with a fixed and predetermined growth rate. Let me clear this chart. Compare that prior graph to this new one that shows projected sales numbers versus actual sales numbers. These lines show much more variation. Now what's the difference? The projections are based on linear formulas, that are fixed in their logic and pre-determined. The actuals show the kind of random behavior you see in a real marketplace. Let me clear that chart to show you another change that's been made in this model design. I extended the decision variables and key assumptions ranges to allow for per period estimates, rather than applying a single annual assumption about growth or charges for returns. That does help surface some hidden features in the numbers. For example, the model now allows for assumptions about sales and return rates that are discreet by time, and reflect a seasonal burst of activity at the end of the calendar year. But that doesn't change the underlying determinism of the model. In our next module, we'll look at ways to move beyond these deterministic models, to incorporate more real world variability in our forecasts. Now let's summarize Module 2. In this module, we explored approaches to building spreadsheets that changed our electronic ledgers into models. We pulled out of the logic in our spreadsheet formulas, the decisions we are making, and our key assumptions about the business scenario we are in. We made clear the output metrics we are most interested in by putting them together in a specific location on the model. We organized our model so that variables that applied in multiple locations were located in only one place. We used range names to clarify the logic in our formulas. And then, using these new structures, we conducted what if analysis to see how changes in our assumptions about the business environment might affect our outcomes. We learned how to collect these changes and assumptions and decisions as scenarios for reuse at a later time. We learned how to test the sensitivity of the model's outputs to changes in decision variables and assumptions. Following that technique, we identified the relatively more important variables for the focus of our analysis. Finally, we looked at the limitations of the models that are based on simple linear functions and that are deterministic. Our future modules will explore ways to get beyond those limitations.