The following data represent the population of the United

Chapter 5, Problem 7

(choose chapter or problem)

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. 344 CHAPTER 5 Exponential and Logarithmic Functions Year Population 1900 1910 1920 1930 1940 1950 1960 76,212,168 92,228,496 106,021,537 123,202,624 132,164,569 151,325,798 1970 1980 179,323,175 203,302,031 226,542,203 1990 248,709,873 2010 308,745,538 2000 281,421,906 Source: U.S. Census Bureau (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 2012. (f) When will the United States population be 350,000,000? (g) Compare actual U.S. Census figures to the predictions found in parts (e) and (f). Discuss any differences