Chapter 5.9, Problem 7AYU

Population Model 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.

$\begin{array}{cc}Year& Population\\ 1900& 76,212,168\\ 1910& 92,228,496\\ 1920& 106,021,537\\ 1930& 123,202,624\\ 1940& 132,164,569\\ 1950& 151,325,798\\ 1960& 179,323,175\\ 1970& 203,302,031\\ 1980& 226,542,203\\ 1990& 248,709,873\\ 2000& 281,421,906\\ 2010& 308,745,538\end{array}$

Source: U.S. Census Bureau

Using a graphic utility, draw a scatter plot of the data using years since $1900$ as the independent variable and population as the dependent variable.

Using a graphic utility, build a logistic model from the data.

Using a graphic utility, graph the function found in part (b) on the scatter plot.

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

Use the function found in part (b) to predict the population of the United States in $2012$.

When will the United States population be $350,000,000$?

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