
Concept explainers
The graphing calculator screen displays an exponential function that models the U.S. population age 65 and over, y, in millions, x years after 1899. Use this information to solve Exercises 31-32.
Refer to the graph showing the U.S. population age 65 and over and the graphing calculator screen on the previous page.
a. Explain why an exponential function was used to model the population data.
b. Use the graphing calculator screen to express the model in function notation, with numbers rounded to three decimal places.
c. According to the model in part (b), how many Americans age 65 and over were there in 2000? Use a calculator with a
d. According to the model in part (b), how many Americans age 65 and over will there be in 2030? Round to one decimal place. Does this rounded number overestimate or underestimate the 2030 population projection displayed by the bar graph? By how much?

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