Question

a survey approximates the number of americans that are age 65 and older and projects that by the year 2050, approximately 83.3 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 = 3.5330737925 b = 1.02285115 a. an exponential function was used because exponential functions are always more accurate than linear functions. d. an exponential function was used because there are too many data points to use a linear function. 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 an exponential function is $y = a\cdot b^x$. Given $a = 3.5330737925$ and $b = 1.02285115$.

Step2: Round the values

Round $a$ to three decimal places: $a\approx3.533$. Round $b$ to three decimal places: $b\approx1.023$.

Step3: Write the function in function - notation

Substitute the rounded values of $a$ and $b$ into the function $y = a\cdot b^x$. In function - notation $f(x)=a\cdot b^x$, so $f(x)=3.533\times1.023^x$.

Answer:

$f(x)=3.533\times1.023^x$