Historical United States Population

The table below shows the U.S. population (as determined by the decennial census), from the first census in 1790 up to 1890.

Year	Population (millions)
1790	3.93
1800	5.31
1810	7.24
1820	9.64
1830	12.86
1840	17.06
1850	23.19
1860	31.44
1870	38.56
1880	50.19
1890	62.98

1. Graph the data. What relationship appears to exist between the year and the population over this period?

2. Using linear regression, find the line which best fits this data. How good is the fit (i.e. what is the correlation)?

3. Graph the log plot of the data. What relationship appears to exist between the year and the logarithm of the population?

4. Using linear regression and the log plot, find the exponential function which best fits the data. How good is the fit? According to this model, how often will the U.S. population double?

5. Which model is better - linear or exponential? Graph the better model with the data. For what years is the fit best? Worst?

6. Consider the data just from 1790 to 1860. Graph the log plot for this range, use linear regression to find the exponential function which best fits those data points. How good is the fit? Is it better or worse than the model you found in part 4? What population does the new model predict for 1870? How does this differ from the census data? Can you think of any good explanation for the discrepancy?

7. Using your model from part 5, predict the population in 2000. The 2000 Census estimates that the U.S. population is 281,421,906. How accurate was your prediction? Discuss some factors which might help explain the discrepancy.