## U.S. Population 1790-1860

Year | Population ( in thousands) |
Change in Population ( in thousands) |
Successive Population Quotients |
---|---|---|---|

1790 | 3929 | ---- | ---- |

1800 | 5308 | 5308 - 3929 = 1379 | $\frac{5308}{3929} \approx 1.351$ |

1810 | 7240 | 7240 - 5308 = 1932 | $\frac{7240}{5308} \approx 1.364$ |

1820 | 9638 | ||

1830 | 12,866 | ||

1840 | 17,069 | ||

1850 | 23,192 | ||

1860 | 31,443 |

**Source:** http://en.wikipedia.org/wiki/Demographic_history_of_the_United_States#Historical_population

- Complete the table. In the fourth column, round to the thousandths place.
- Would a linear function be an appropriate model for the relationship between the U.S. population and the year? Explain why or why not.
- Would an exponential function be an appropriate model for the relationship between the U.S. population and the year? Explain why or why not.
- Heather decides to use an exponential function of the form $y=a \cdot b^x$ to model the relationship. She chooses 1.359 for the value of $b$. What meaning does this value have in the context of these data?
- Use Heather's base value and the population in 1860 to predict the U.S. population in the year 1900.