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. expreg y = a*b^x a = 3.3233833027 b = 1.023463082 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. b. use the graphing calculator screen to express the model in function notation, with numbers rounded to three decimal places. f(x) =

Explanation:

Step1: Identify the exponential - function form

The general form of the exponential function is $y = a\cdot b^x$. Given $a = 3.3233833027$ and $b = 1.023463082$.

Step2: Round the values

Round $a$ and $b$ to three decimal places. $a\approx3.323$ and $b\approx1.023$.

Step3: Write the function in function - notation

Substitute the rounded values into $y = a\cdot b^x$ and write it as $f(x)$. So $f(x)=3.323\times1.023^x$.

Answer:

$f(x)=3.323\times1.023^x$