So summarizing what we've done in this first module, we started off talking about uses for models. The two key uses for these quantitative models tend to be in predictive analytics, in making predictions, and forecasts, and also in doing optimization problems. We've seen the steps involved in the modelling process. It starts off by defining some variables, identifying the scope of the model. There's a formulation stage. But you must not forget that there is an entire validation and sensitivity analysis phase as well. If your model works well, that's good. But typically it's not going to work well the first time around. That's why I put a feedback loop in the modeling process. So the model never in my experience works perfectly straight out of the box the first time around. We're very iterative, we go back and we revisit some of the assumptions behind the model. We might look for additional terms to put into the model. We might reformulate the model. There's an iterative process there. Ultimately, we feel that the model validates well and we performed our sensitivity analysis. We then ask ourself the key question, is the model fit for purpose? And I've used that language very purposely there because I have not said, is the model right or is it wrong. Because models are never absolutely right because they are almost by definition, simplifications of a much more complicated real world. The key question is, is the model fit for purpose, is it useful at helping me answer questions? In other words, is it going to be a useful decision support tool. So don't forget to validate your model. We've discussed various types of models. That was the language that I introduced in modeling. We talked about deterministic and stochastic. We talked about discrete and continuous. We talked about static and dynamic models. So those terms are important to understand because you might at some point have a conversation as you create more of these models with someone and say, well did you create a discrete time or continuous time model? And being able to understand those words is very helpful if you want to be able to participate in those conversations. The final part of the module was reviewing some essential mathematics in particular seeing the functions that we're going to be using as we create our quantitative models there were four key functions. Linear, power, exponential, and log. And from a modeling point of view, what you want to understand about these functions is how they relate changes in the input to changes in the output and whether or not those changes are being thought of in absolute terms or relative terms. So recall, a straight line is characterized by its constant slope. And that tells us that absolute changes in X are always accompanied with the same absolute change in Y of M. That's what the slope of M equals. Whereas if we had a power function, then we would have a 1% change in X is associated with an approximate M% change in Y. So percent change in X is percent change in Y. And you simply have to think about and understand your business process and ask yourself, well, on which type of change is this process most readily modeled? In terms of absolute change or percent change. And by doing that, you're able to think which of these functions should be used in the model.