SOLUTION: 46. Based on data from the U.S. Census Bureau, 8.4% of U.S. workers in 1992 earned over $100,000. In 2000, 13.4% of U.S. workers earned over $100,000. a. Find a linear function t

Question 53330This question is from textbook Algebra 1
: 46. Based on data from the U.S. Census Bureau, 8.4% of U.S. workers in 1992 earned over $100,000. In 2000, 13.4% of U.S. workers earned over $100,000.
a. Find a linear function that gives the percent of workers earned in excess of $100,000 for a given year.
b. In 1998, there were approximately 104,000,000 workers in the U.S. According to your model, how many of these workers earned over $100,000? This question is from textbook Algebra 1

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Based on data from the U.S. Census Bureau, 8.4% of U.S. workers in 1992 earned over $100,000. In 2000, 13.4% of U.S. workers earned over $100,000.
a. Find a linear function that gives the percent of workers earned in excess of $100,000 for a given year.
The year is the independent variable; the percent is the dependent variable.
Percent= slope (year)+ b
You have two points: (92,8.4), (100,13.4)
m=[13.4-8.4]/[100-92]=5/8
Using the point (100,13.4) and m you can solve for b as follows:
13.4=(5/8)100+b
13.4= 62.5+b
b=-49.1
EQUATION:
Percent= (5/8)(year)-49.1

b. In 1998, there were approximately 104,000,000 workers in the U.S. According to your model, how many of these workers earned over $100,000?
1st find the percent using the equation from part "a".
Percent = (5/8)(98)-49.1
Percent = 12.51%
2nd: Find the number of workers using the percent.
12.51% (104,000,000)=12,636,000 workers earned over $100,000 in '98.
Cheers,
Stan H.

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