The following data represent the population of the United States. An ecologist is interested in building a model that describes the population of the United States.

Year …………………………….. Population

1900 ……………………………. 76,212,168

1910 ……………………………. 92,228,496

1920 ……………………………. 106,021,537

1930 ……………………………. 123,202,624

1940 ……………………………. 132,164,569

1950 ……………………………. 151,325,798

1960 ……………………………. 179,323,175

1970 ……………………………. 203,302,031

1980 ……………………………. 226,542,203

1990 ……………………………. 248,709,873

2000 ……………………………. 281,421,906

(a) Using a graphing utility, draw a scatter diagram of the data using years since 1900 as the independent variable and population as the dependent variable.

(b) Using a graphing utility, build a logistic model from the data.

(c) Using a graphing utility, draw the function found in part (b) on the scatter diagram.

(d) Based on the function found in part (b), what is the carrying capacity of the United States?

(e) Use the function found in part (b) to predict the population of the United States in 2004.

(f) When will the United States population be 300,000,000?

(g) Compare actual U.S. Census figures to the predictions found in parts (e) and (f). Discuss any differences.