Question

A 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 = a-b^xClick the icon to view the bar graph.a 3.4781166081b= 1.023023196b. Use the graphing calculator screen to express the model in function notation, with numbers rounded to three decimal places.f(x)= 3.478(1.023)*c. According to the model in part (b), how many Americans age 65 and over were there in 2010? Use a graphing calculator.million(Type an integer or a decimal rounded to one decimal place as needed.).

Answer 1

Solution

- The population function is:

$\begin{gathered} f(x)=3.478(1.023)^x \\ where, \\ x\text{ is the number of years after 1899} \end{gathered}$

- Thus, to find the number of people, 65 year olds and older, present at 2010, we perform the following steps:

$\begin{gathered} x=2010-1899 \\ x=111 \\ \\ \therefore f(x)=3.478(1.023)^{111} \\ \\ f(x)=43.4\text{ Million} \end{gathered}$

Final Answer

The answer is 43.4 Million