Functions of Two Variables and Contour Diagrams

The most difficult idea from sections 9.1 and 9.2 was probably the Cobb-Douglass Production Model. It is a completely new concept to me, but the example about a small company going through expansion, was very helpful. There is the idea of holding one variable constant while seeing how the other changes. The other example modeling the production of the US economy was precise. apparently the equation P= 1.01L^0.75K^0.25 is very accurate, but how was this equation developed?

I see the class having difficulty with the contours on a topographical map. Contour diagrams are common in maps and weather charts, but honestly i never analyzed the functions before. For example figure 9.10 I have never seen how a pass between two mountains was represented.