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. (type an integer or a decimal rounded to one - decimal place as needed.) does this rounded number overestimate or underestimate the 2010 population displayed by the bar graph? by how much? choose the correct answer below and fill in the answer box to complete your choice (type an integer or decimal rounded to one decimal place as needed.) a. the rounded number overestimates the 2010 population by 0.2 million. b. the rounded number underestimates the 2010 population by million. d. according to the model in part (b), how many americans age 65 and over will there be in 2020? million (type an integer or decimal rounded to one decimal place as needed.)

Explanation:

Step1: Determine the value of x for 2020

Since x is years after 1899, for 2020, $x = 2020 - 1899=121$.

Step2: Use the exponential - function formula

The exponential function is $y = a\cdot b^{x}$, where $a = 3.5933424683$ and $b = 1.022647483$. Substitute $x = 121$ into the formula: $y=3.5933424683\times(1.022647483)^{121}$.

Step3: Calculate the result

Using a calculator, $(1.022647483)^{121}\approx15.779$, then $y = 3.5933424683\times15.779\approx56.7$.

Answer:

56.7