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

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

Natural Science Carbon monoxide combines with the hemoglobin of the blood to form carboxyhemoglobin (COHb), which reduces the transport of oxygen to tissue. A 4%-to-6% COHb level in the blood (typical for smokers) can cause symptoms such as alterations in blood flow, visual impairment, and poorer vigilance. When 50 ≤ x ≤ 100, the equation T = .00787x2 − 1.528x + 75.89 approximates the exposure time T(in hours) necessary to reach this 4%-to-6% level, where x is the amount of carbon monoxide present in the air in parts per million (ppm).†

(a) A kerosene heater or a room full of smokers is capable of producing 50 ppm of carbon monoxide. How long would it take for a nonsmoking person to start feeling the aforementioned symptoms under such conditions?

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(b) What carbon monoxide concentration will cause a person to reach a 4%-to-6% COHb level in three hours?

†U.S. Department of Energy.

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.