Problem

Use a graphing calculator to work Exercise. (See Examples 1 and 2.)Physical Science The su...

Use a graphing calculator to work Exercise. (See Examples 1 and 2.)

Physical Science The surface area of the right square pyramid in the figure is given by . If the pyramid has height 10 feet and surface area 100 square feet, what is the length of a side b of its base?

Example 1

Use a graphical root finder to solve x3 − 5x + 1 = 0.

Solution

First, graph y = x3 − 5x + 1. The x-intercepts of this graph are the solutions of the equation. To find these intercepts, look for “root” or “zero” in the appropriate menu.* Check your instruction manual for the proper syntax. A typical root finder (see Figure 1) shows that two of the solutions (x-intercepts) are x ≈ .2016 and x ≈ 2.1284. For the third solution, see the problem at the side.

*CALC or TI-84+, GRAPH MATH on TI-86, G-SOLV on Casio.

Example 2

Health The percentage y of 12th graders who have ever tried an illicit drug is approximated by

where x = 1 corresponds to the year 1991.* In what year was the percentage of 12th graders who tried illicit drugs the greatest? What was that percentage?

Solution

The graph of y = −.00374x3 − .0591x2 + 2.534x + 38.21 is shown in Figure 2. The highest percentage of 12th graders who tried illicit drugs corresponds to the highest point on this graph. To find this point, look for “maximum” or “max” or “extremum” in the same menu as the graphical root finder. Check your instruction manual for the proper syntax. A typical maximum finder (Figure 3) shows that the highest point has approximate coordinates (10.66, 53.98). The first coordinate is the year and the second is the percentage. So the largest percentage of 12th graders who tried illicit drugs (about 53.98%) occurred in mid-2000 (x ≈ 10.66).

FIGURE 1

FIGURE 2

FIGURE 3

*L. D. Johnston, P. M. O’Malley, J. G. Bachman, and J. E. Schulenberg. “Teen smoking resumes decline.” Ann Arbor. MI: University of Michigan News Service [Online], Available: www.monitoringthefuture.org.

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