Question

Answer question BA survey approximates the number of Americans that are age 65 and older and projects that by the year 2050, approximately 82.4 million Americans will be at least65. 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.ExpRegy = ab'xClick the icon to view the bar grapha = 3.4781166081b= 1.023023196a. Explain why an exponential function was used to model the population data.OA. An exponential function was used because population is always modeled using exponential functions.B. An exponential function was used because exponential functions are always more accurate than linear functions.C. An exponential function was used because there are too many data points to use a linear function.D. An exponential function was used because the data in the bar graph is increasing more and more rapidly.b. Use the graphing calculator screen to express the model in function notation, with numbers rounded to three decimal places.

Answer 1

- The formula for the exponential function is:

`y=ab^x`

- Thus, the function required is

`\begin{gathered} a=3.4781166...\approx3.478\text{ \lparen To 3 dp\rparen} \\ b=1.0230231...\approx1.023\text{ \lparen To 3dp} \\ \\ \\ y=3.478(1.023)^x \end{gathered}`