In Example 1, we used two data points and an exponential function to model the population of the United States from 1970 through 2010. The data are shown again in the table. Use all five data points to solve Exercises 66–70.

Data from example 1

The graph in Figure 4.22 shows the U.S. population, in millions, for five selected years from 1970 through 2010. In 1970, the U.S. population was 203.3 million. By 2010, it had grown to 308.7 million.

Figure 4.22

a. Use your graphing utility’s exponential regression option  to obtain a model of the form y = ab^x that fits the data.  How well does the correlation coefficient, r, indicate that  the model fits the data?

b. Rewrite the model in terms of base e. By what percentage  is the population of the United States increasing each  year?

x, Number of Years after 1969 1 (1970) 11 (1980) 21 (1990) 31 (2000) 41 (2010) y, U.S. Population (millions) 203.3 226.5 248.7 281.4 308.7