The representation of women in leadership positions in our economy has changed dramatically in the past 20 years. In this application we'll investigate whether some predictions made in 1997 are still valid. In January 1997, Working Woman made the following points about the U.S. economy and the place of women in the economy. . . The telecommunications industry employs more people than the auto and auto parts industries combined. More Americans make semiconductors than make construction equipment. Almost twice as many Americans make surgical and medical instruments as make plumbing and heating products. The ratio of male to female knowledge workers (engineers, scientists, technicians, professionals, and senior managers) was 3 to 2 in 1983. The table, which gives the numbers (in millions) of male and female knowledge workers from 1983 to 1997, shows how that ratio is changing. . Year Year 1983 1984 1985 1986 1987 1988 1989 1990 Female Knowledge Workers (millions) 11.0 11.6 12.3 12.9 13.6 14.3 15.3 15.9 Male Knowledge Workers (millions) 15.4 15.4 16.3 16.7 16.8 17.6 18.1 18.6 1991 1992 1993 1994 1995 1996 1997 Female Knowledge Workers (millions) 16.1 16.7 17.3 18.0 18.5 19.0 19.5 Male Knowledge Workers (millions) 18.4 18.66 18.7 19.0 19.8 19.6 19.8 To compare how the growth in the number of female knowledge workers compares with that of male knowledge workers, do the following: 1. Find a logarithmic equation (with x = 0 representing 1980) that models the number of females and find a logarithmic equation (with x = 0 representing 1980) that models the number of males. 2. Use the models found in (1) to find the rate of growth with respect to time of (a) the number of female knowledge worke and (b) male knowledge workers. 3. Compare the two rates of growth in the year 2000 and determine which rate is larger. 4. If these models indicate that it is possible for the number of females to equal the number of males, during what year do they indicate that this will occur? 5. Research this topic on the Internet to determine whether the trends of your models are supported by current data. Be sure to cite your sources and include recent data. The representation of women in leadership positions in our economy has changed dramatically in the past 20 years. In this application we'll investigate whether some predictions made in 1997 are still valid. In January 1997, Working Woman made the following points about the U.S. economy and the place of women in the economy. . . The telecommunications industry employs more people than the auto and auto parts industries combined. More Americans make semiconductors than make construction equipment. Almost twice as many Americans make surgical and medical instruments as make plumbing and heating products. The ratio of male to female knowledge workers (engineers, scientists, technicians, professionals, and senior managers) was 3 to 2 in 1983. The table, which gives the numbers (in millions) of male and female knowledge workers from 1983 to 1997, shows how that ratio is changing. . Year Year 1983 1984 1985 1986 1987 1988 1989 1990 Female Knowledge Workers (millions) 11.0 11.6 12.3 12.9 13.6 14.3 15.3 15.9 Male Knowledge Workers (millions) 15.4 15.4 16.3 16.7 16.8 17.6 18.1 18.6 1991 1992 1993 1994 1995 1996 1997 Female Knowledge Workers (millions) 16.1 16.7 17.3 18.0 18.5 19.0 19.5 Male Knowledge Workers (millions) 18.4 18.66 18.7 19.0 19.8 19.6 19.8 To compare how the growth in the number of female knowledge workers compares with that of male knowledge workers, do the following: 1. Find a logarithmic equation (with x = 0 representing 1980) that models the number of females and find a logarithmic equation (with x = 0 representing 1980) that models the number of males. 2. Use the models found in (1) to find the rate of growth with respect to time of (a) the number of female knowledge worke and (b) male knowledge workers. 3. Compare the two rates of growth in the year 2000 and determine which rate is larger. 4. If these models indicate that it is possible for the number of females to equal the number of males, during what year do they indicate that this will occur? 5. Research this topic on the Internet to determine whether the trends of your models are supported by current data. Be sure to cite your sources and include recent data