example 2 u.s. foreign-born population chapter 6.1 the table gives the percents of u.s. population...

example 2 U.S. Foreign-Born Population

Chapter 6.1

The table gives the percents of U.S. population that were foreign born for the years1900–2005.

YearsForeign Born

(%)Years

Foreign Born (%)

1900 13.6 1960 5.4

1910 14.7 1970 4.8

1920 13.2 1980 6.2

1930 11.6 1990 8.0

1940 8.8 2000 10.4

1950 6.9 2005 11.7

The data can be modeled by the cubic function

where y is the percent and x is the number of years after 1900.

3 2( ) 0.0000503 0.00560 0.0165 14.308f x x x x

2009 PBLPathways

2009 PBLPathways

The table gives the percents of U.S. population that were foreign born for the years1900–2005.

YearsForeign Born

(%)Years

Foreign Born (%)

1900 13.6 1960 5.4

1910 14.7 1970 4.8

1920 13.2 1980 6.2

1930 11.6 1990 8.0

1940 8.8 2000 10.4

1950 6.9 2005 11.7

The data can be modeled by the cubic function

where y is the percent and x is the number of years after 1900.

3 2( ) 0.0000503 0.00560 0.0165 14.308f x x x x

2009 PBLPathways

a. Graph the data points and this function on the same axes, using the window [0, 110] by [0, 16].

b. Use the model and technology to find the approximate percent of the U.S. population that was foreign born in 1954.

c. Interpret the y-intercept of the graph of this function.

d. Find the local maximum and the local minimum. What do these two points on the graph indicate?

e. Over what interval is the function (and thus the percent) decreasing? What does this mean?

2009 PBLPathways

a. Graph the data points and this function on the same axes, using the window [0, 110] by [0, 16].

YearsForeign Born

(%)Years

Foreign Born (%)

1900 13.6 1960 5.4

1910 14.7 1970 4.8

1920 13.2 1980 6.2

1930 11.6 1990 8.0

1940 8.8 2000 10.4

1950 6.9 2005 11.7

3 2( ) 0.0000503 0.00560 0.0165 14.308f x x x x

2009 PBLPathways

a. Graph the data points and this function on the same axes, using the window [0, 110] by [0, 16].

Years after 1900

Foreign Born (%)

Years after 1900

Foreign Born (%)

0 13.6 60 5.4

10 14.7 70 4.8

20 13.2 80 6.2

30 11.6 90 8.0

40 8.8 100 10.4

50 6.9 105 11.7

3 2( ) 0.0000503 0.00560 0.0165 14.308f x x x x

2009 PBLPathways

a. Graph the data points and this function on the same axes, using the window [0, 110] by [0, 16].

3 2( ) 0.0000503 0.00560 0.0165 14.308f x x x x

2009 PBLPathways

b. Use the model and technology to find the approximate percent of the U.S. population that was foreign born in 1954.

3 2( ) 0.0000503 0.00560 0.0165 14.308f x x x x

2009 PBLPathways

b. Use the model and technology to find the approximate percent of the U.S. population that was foreign born in 1954.

3 2( ) 0.0000503 0.00560 0.0165 14.308f x x x x

(54) 6.79f ?

2009 PBLPathways

b. Use the model and technology to find the approximate percent of the U.S. population that was foreign born in 1954.

3 2( ) 0.0000503 0.00560 0.0165 14.308f x x x x

(54) 6.79f ?

54

2009 PBLPathways

b. Use the model and technology to find the approximate percent of the U.S. population that was foreign born in 1954.

3 2( ) 0.0000503 0.00560 0.0165 14.308f x x x x

(54) 6.79f ?

54

6.79

2009 PBLPathways

b. Use the model and technology to find the approximate percent of the U.S. population that was foreign born in 1954.

3 2( ) 0.0000503 0.00560 0.0165 14.308f x x x x

(54) 6.79f

54

6.79

2009 PBLPathways

c. Interpret the y-intercept of the graph of this function.

3 2( ) 0.0000503 0.00560 0.0165 14.308f x x x x

2009 PBLPathways

c. Interpret the y-intercept of the graph of this function.

3 2( ) 0.0000503 0.00560 0.0165 14.308f x x x x

(0, 14.308)(0) 14.308f

2009 PBLPathways

d. Find the local maximum and the local minimum. What do these two points on the graph indicate?

3 2( ) 0.0000503 0.00560 0.0165 14.308f x x x x

2009 PBLPathways

d. Find the local maximum and the local minimum. What do these two points on the graph indicate?

3 2( ) 0.0000503 0.00560 0.0165 14.308f x x x x

(1.50, 14.32)

(72.72, 5.24)

2009 PBLPathways

e. Over what interval is the function (and thus the percent) decreasing? What does this mean?

3 2( ) 0.0000503 0.00560 0.0165 14.308f x x x x

(1.50, 14.32)

(72.72, 5.24)

2009 PBLPathways

e. Over what interval is the function (and thus the percent) decreasing? What does this mean?

3 2( ) 0.0000503 0.00560 0.0165 14.308f x x x x

(1.50, 14.32)

(72.72, 5.24)

As x gets larger

: 1.50 72.72x

y decreases

: 14.32 5.24y