1. The fallout, V (in kilograms per square kilometer), from a volcanic explosion depends on the distance, d, from the volcano and the time, t, since the explosion.

V = f(d,t) = (t)e^-d

(a) Draw two graphs that illustrate the function V . For the first, graph the cross-sections of V where d = 0, d = 1, and d = 2. For the second graph, provide cross-sections where t = 0, t = 1, and t = 2. (See 8.1 Example 4 of graphing cross-sections).

(b) Describe how changing t changes V. Answers should address what the model says about the fallout of a volcano.

(c) Describe how changing d changes V. Again, refer to the model.

2) Draw a contour graph representing two hills next to each other. Draw a path (different color) from the top of one hill to the top of the other. Describe the partial derivatives at different points along that path.