example 4 Foreign-Born Population

Chapter 6.2

The percents of U.S. population that were foreign born for selected years during 1900–2005 are shown in the table.

Year Percent

1900 13.6

1910 14.7

1920 13.2

1930 11.6

1940 8.8

1950 6.9

1960 5.4

1970 4.8

1980 6.2

1990 8.0

2000 10.4

2005 11.7

a. Create a scatter plot for the data, using the number of years after 1900 as the input x and the percent as the output y.

b. Find a cubic function to model the data and graph the function on the same axes with the data points. Round coefficients to seven decimal places.

c. Find a quartic function to model the data and graph the function on the same axes with the data points. Round coefficients to seven decimal places.

d. Use the graphs of the equations reported in parts (b) and (c) to determine which function is the better fit for the data.

2009 PBLPathways

2009 PBLPathways

Year Percent

1900 13.6

1910 14.7

1920 13.2

1930 11.6

1940 8.8

1950 6.9

1960 5.4

1970 4.8

1980 6.2

1990 8.0

2000 10.4

2005 11.7

a. Create a scatter plot for the data, using the number of years after 1900 as the input x and the percent as the output y.

b. Find a cubic function to model the data and graph the function on the same axes with the data points. Round coefficients to seven decimal places.

c. Find a quartic function to model the data and graph the function on the same axes with the data points. Round coefficients to seven decimal places.

d. Use the graphs of the equations reported in parts (b) and (c) to determine which function is the better fit for the data.

The percents of U.S. population that were foreign born for selected years during 1900–2005 are shown in the table.

2009 PBLPathways

Year Percent

1900 13.6

1910 14.7

1920 13.2

1930 11.6

1940 8.8

1950 6.9

1960 5.4

1970 4.8

1980 6.2

1990 8.0

2000 10.4

2005 11.7

a. Create a scatter plot for the data, using the number of years after 1900 as the input x and the percent as the output y.

The percents of U.S. population that were foreign born for selected years during 1900–2005 are shown in the table.

2009 PBLPathways

Years after 1900 Percent

0 13.6

10 14.7

20 13.2

30 11.6

40 8.8

50 6.9

60 5.4

70 4.8

80 6.2

90 8.0

100 10.4

105 11.7

a. Create a scatter plot for the data, using the number of years after 1900 as the input x and the percent as the output y.

The percents of U.S. population that were foreign born for selected years during 1900–2005 are shown in the table.

2009 PBLPathways

Years after 1900 Percent

0 13.6

10 14.7

20 13.2

30 11.6

40 8.8

50 6.9

60 5.4

70 4.8

80 6.2

90 8.0

100 10.4

105 11.7

a. Create a scatter plot for the data, using the number of years after 1900 as the input x and the percent as the output y.

x

y

The percents of U.S. population that were foreign born for selected years during 1900–2005 are shown in the table.

2009 PBLPathways

b. Find a cubic function to model the data and graph the function on the same axes with the data points. Round coefficients to seven decimal places.

x

y

3 20.0000503 0.0056014 0.0165213 14.3080156y x x x

x

y

The percents of U.S. population that were foreign born for selected years during 1900–2005 are shown in the table.

2009 PBLPathways

b. Find a cubic function to model the data and graph the function on the same axes with the data points. Round coefficients to seven decimal places.

x

y

3 20.0000503 0.0056014 0.0165213 14.3080156y x x x

x

y

The percents of U.S. population that were foreign born for selected years during 1900–2005 are shown in the table.

2009 PBLPathways

b. Find a cubic function to model the data and graph the function on the same axes with the data points. Round coefficients to seven decimal places.

x

y

3 20.0000503 0.0056014 0.0165213 14.3080156y x x x

The percents of U.S. population that were foreign born for selected years during 1900–2005 are shown in the table.

2009 PBLPathways

c. Find a quartic function to model the data and graph the function on the same axes with the data points. Round coefficients to seven decimal places.

x

y

4 3 20.0000008 0.0002196 0.0167097 0.2503283 13.5809230y x x x x

x

y

The percents of U.S. population that were foreign born for selected years during 1900–2005 are shown in the table.

2009 PBLPathways

c. Find a quartic function to model the data and graph the function on the same axes with the data points. Round coefficients to seven decimal places.

x

y

4 3 20.0000008 0.0002196 0.0167097 0.2503283 13.5809230y x x x x

x

y

The percents of U.S. population that were foreign born for selected years during 1900–2005 are shown in the table.

2009 PBLPathways

c. Find a quartic function to model the data and graph the function on the same axes with the data points. Round coefficients to seven decimal places.

x

y

4 3 20.0000008 0.0002196 0.0167097 0.2503283 13.5809230y x x x x

The percents of U.S. population that were foreign born for selected years during 1900–2005 are shown in the table.

2009 PBLPathways

d. Use the graphs of the equations reported in parts (b) and (c) to determine which function is the better fit for the data.

x

y

x

y

Cubic Function Quartic Function

x

The percents of U.S. population that were foreign born for selected years during 1900–2005 are shown in the table.