A survey approximates the number of Americans that are age 65 and older and projects that by the year 2050, approximately 82.6 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. B ExpReg y = a-b^x a = 3.363809536 b = 1.023357735 a. Explain why an exponential function was used to model the population data. An exponential function was used because the data in the bar graph is increasing more and more rapidly. OB. An exponential function was used because population is always modeled using exponential functions. OC. An exponential function was used because there are too many data points to use a linear function. OD. An exponential function was used because exponential functions are always more accurate than linear functions. b. Use the graphing calculator screen to express the model in function notation, with numbers rounded to three decimal places. f(x) =

A survey approximates the number of Americans that are age 65 and older and projects that by the year 2050, approximately 82.6 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. B ExpReg y = a-b^x a = 3.363809536 b = 1.023357735 a. Explain why an exponential function was used to model the population data. An exponential function was used because the data in the bar graph is increasing more and more rapidly. OB. An exponential function was used because population is always modeled using exponential functions. OC. An exponential function was used because there are too many data points to use a linear function. OD. An exponential function was used because exponential functions are always more accurate than linear functions. b. Use the graphing calculator screen to express the model in function notation, with numbers rounded to three decimal places. f(x) =

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

A survey approximates the number of Americans that are age 65 and older and projects that by the year 2050,
approximately 82.6 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.
最重
ExpReg
y = a-b^x
a = 3.363809536
b = 1.023357735
a. Explain why an exponential function was used to model the population data.
A. An exponential function was used because the data in the bar graph is increasing more and more rapidly.
OB. An exponential function was used because population is always modeled using exponential functions.
OC. An exponential function was used because there are too many data points to use a linear function.
OD. An exponential function was used because exponential functions are always more accurate than linear
functions.
b. Use the graphing calculator screen to express the model in function notation, with numbers rounded to three
decimal places.
f(x) =

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C. According to the model in part.(b) , how many Americans age 65 and over were there in 2010? Use a graphing calculator.

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