4 Determining Change: Derivatives

Project 4.1: Fertility Rates

Setting

The Statistical Abstract of the United States (1995 Edition) reports the following fertility rates for whites in the United States.

TABLE 4.51

 Year Fertility rate 1970 2385 1972 1907 1974 1749 1976 1652 1978 1668 1980 1773 1982 1767 1984 1749 1986 1776 1988 1857 1990 2003 1992 1994 1994 1976

1. Find a table of fertility rate data in a current edition of the Statistical Abstract, and summarize in your own words the meaning of "fertility rate." Assign units to the fertility rate column in Table 4.51.
2. Find a piecewise model that fits the given fertility rate data. Write the derivative function for this model. Construct a table of fertility rates and the rate of change of fertility rates for all years from 1970 through 1994. Discuss the points at which the derivative of your model does not exist (and why it does not exist), and explain how you estimated the rates of change at these points.
3. Using the data in a current edition of the Statistical Abstract, complete the same analysis as in Task 2 for the fertility rates for blacks in the United States.
4. Add 1996 and any other recent data for the fertility rate of whites. (Note: Recent editions of the Statistical Abstract occasionally update older data points. Therefore, you should check the data for pre-1996 as well and change any updated values so that your data agree with the most recent Statistical Abstract.) Find a piecewise model for the updated data. Use this new model to calculate the rates of change that occurred in the years since 1995.

Reporting

Write a report discussing your findings and their demographical impact. Include your mathematical computations as an appendix.