Question

a survey approximates the number of americans that are age 65 and older and projects that by the year 2050, approximately 82.7 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 = 3.5933424683 b = 1.022647483 f(x)=3.593·1.023^x 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.)

Explanation:

Step1: Calculate the value of x

The year is 2010, and x is the number of years after 1899. So $x = 2010 - 1899=111$.

Step2: Substitute x into the function

The function is $y = 3.593\times1.023^{x}$. Substitute $x = 111$ into it, we get $y = 3.593\times1.023^{111}$.
Using a graph - ing calculator to calculate $1.023^{111}\approx13.277$, then $y = 3.593\times13.277\approx47.7$.

Answer:

47.7