Question

a survey approximates the number of americans that are age 65 and older and projects that by the year 2050, approximately 81.7 million americans will be at least 65. the bar graph shows the estimated number of americans with projected figures for the year 2020 and beyond. a 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 (a)-(d) below. click the icon to view the bar graph. a. explain why an exponential function was used to model the population data. a. an exponential function was used because exponential functions are always more accurate than linear functions. b. an exponential function was used because there are too many data points to use a linear function. c. an exponential function was used because population is always modeled using exponential functions. d. an exponential function was used because the data in the bar graph is increasing more and more rapidly.

Explanation:

Exponential functions are used to model data that grows or decays at a rate proportional to its current value. In population - related data, when the growth is accelerating (increasing more and more rapidly), an exponential function is a good fit. Linear functions have a constant rate of change, and exponential functions are not always more accurate than linear functions in all cases. The number of data points is not the main reason for choosing an exponential function over a linear one, and population is not always modeled with exponential functions. Here, the bar - graph data shows accelerating growth, which is why an exponential function is appropriate.

Answer:

D. An exponential function was used because the data in the bar graph is increasing more and more rapidly.