Although a graphing calculator is limited to displaying the relationship between only two...

Although a graphing calculator is limited to displaying the relationship between only two variables (for the most part), it has a feature that enables us to see how these two are related with respect to a third. Consider the variation equation from Example 8 in Section 2.6: F = 0.05dv2. If we want to investigate the relationship between fuel consumption and velocity, we can have the calculator display multiple versions of the relationship simultaneously for different values of d. This is accomplished using the “{” and “}” symbols, which are functions to the parentheses. When the calculator sees values between these grouping symbols and separated by commas, it is programmed to use each value independently of the others, graphing or evaluating the relation for each value in the set. We illustrate by graphing the relationship f = 0.05dv2 for three different values of d. Enter the equation on the screen as Y1 = 0.05{10, 20, 30}X2, which tells the calculator to graph the equations Y1 = 0.05(10)X2, Y1 = 0.05(20)X2, and Y1 = 0.05(30)X2 on the same grid. Note that since d is constant, each graph is a parabola. Set the viewing window using the values given in Example 8 as a guide. The result is the graph shown in Figure 2.97, where we can study the relationship between these three variables using the up and down arrows. From our work with the toolbox functions and transformations, we know the widest parabola used the coefficient “10,” while the narrowest parabola used the coefficient “30.” As shown, the graph tells us that at a speed of 15 nautical miles per hour (X = 15), it will take 112.5 barrels of fuel to travel 10 mi (the first number in the list). After pressing the key, the cursor jumps to the second curve, which shows values of X = 15 and Y = 225. This means at 15 nautical miles per hour, it would take 225 barrels of fuel to travel 20 mi. Use these ideas to complete the following exercises:

Figure 2.97

The comparison of distance covered versus fuel consumption at different speeds also makes an interesting study. This time velocities are constant values and the distance varies. On the screen, enter Y1 = 0.05x {510, 20, 306}2. What family of equations results? Use the up/down arrow keys for x = 15 (a distance of 15 mi) to find how many barrels of fuel it takes to travel 15 mi at 10 mph, 15 mi at 20 mph, and 15 mi at 30 mph. Comment on what you notice.