The bar graph shows that compared to a century ago, work in the United States now

Chapter 10, Problem 63

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The bar graph shows that compared to a century ago, work in the United States now involves mostly whitecollar service jobs. Percentage of Total Labor Force The Changing Pattern of Work in the United States, 19002005 Year 40 30 10 20 70 80 90 50 60 White Collar Blue Collar Farming 1900 21 41 38 1920 28 44 28 1940 36 44 20 1960 51 41 8 1980 63 34 3 2005 76 22 2 Source: U.S. Department of Labor The data can be modeled by linear and quadratic functions. 0.5x-y=18 White collar y=0.004x2 +0.23x+41 Blue collar 0.4x+y=35 Farming In each function, x represents the number of years after 1900 and y represents the percentage of the total U.S. labor force. a. Based on the information in the graph, it appears that there was a year when the percentage of whitecollar workers in the labor force was the same as the percentage of blue-collar workers in the labor force. According to the graph, between which two decades did this occur? b. Solve a nonlinear system to determine the year described in part (a). Round to the nearest year. What percentage of the labor force, to the nearest percent, consisted of white-collar workers and what percentage consisted of blue-collar workers? c. According to the graph, for which year was the percentage of white-collar workers the same as the percentage of farmers? What percentage of U.S. workers were in each of these groups? d. Solve a linear system to determine the year described in part (c). Round to the nearest year. Use the models to find the percentage of the labor force consisting of white-collar workers and the percentage consisting of farmers. How well do your answers model the actual data specified in part (c)?