We talked about today linear models, a building block for all modeling, the simplest function that we can use to relate an input to an output and we saw some uses of linear models. We saw a total cost function and we saw a time to produce function. I also briefly talked about linear programming, an optimization technique that is suitable when you have linear models. We talked about growth and decay. Remember, growth is such a fundamental construct business or staying in business. And we talked about grow and decay. First, the in discrete time that was the idea of a geometric series. And we talked about growth and decay in continuous time. We saw when we looked at the geometric series that by creating this quantitative model, we were able to leverage that model in a number of ways and one of the neat things we could do with that model was to work out the sum of a geometric series. We had a nice little formula for that. So that's one of the things that modeling will do for you, it will give you potentially some handy formula that can be used to do speed up calculations. So we did growth and decay in discrete and continuous time. We talked about present and future value. Once you've got a model for growth, you're going to be able to essentially reverse engineer that growth process to say, how much do I need now to obtain a certain amount in the future? And so, given that future amount, what is it worth right now? And so, the reverse engineering of the growth model is essentially what it means to do. A present value calculation. Taking a value in the future and discounting it to the present value. Our models made that straightforward. There are lots of uses for present value in a business setting. One of them, for example, is in valuing an annuity. And another one that I talked about was in lifetime customer value calculations. A lifetime means over a period of time, you're going to have to discount some of those future time periods to understand the current or present value of the customer. And we finished off today by looking at optimization. What I would call classical optimization using calculus and derivatives and that is some times one of the most useful outcomes of having put a quantitative model into place. Yes, we want to understand that business process, but if I have a reasonable model for that business process, I can then exploit that model through the use of optimization to really fine tune, and optimize how my business is working.