A survey approximates the number of Americans that are age 65 and older and projects that by the year​ 2050, approximately

84.184.1

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)dash–​(d)

below.

LOADING...

Click the icon to view the bar graph.

ExpReg

y

equals=

a Subscript ​*​b^x

a

equals=

3.44228238643.4422823864

b

equals=

1.0230844311.023084431

Question content area bottom

Part 1

a.  Explain why an exponential function was used to model the population data.

A.

An exponential function was used because exponential functions are always more accurate than linear functions.

B.

An exponential function was used because the data in the bar graph is increasing more and more rapidly.

Your answer is correct.

C.

An exponential function was used because population is always modeled using exponential functions.

D.

An exponential function was used because there are too many data points to use a linear function.

Part 2

b.  Use the graphing calculator screen to express the model in function​ notation, with numbers rounded to three decimal places.

​f(x)equals=3.442 times 1.023 Superscript x3.442•1.023x

Part 3

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

43.043.0

million

​(Type an integer or a decimal rounded to one decimal place as​ needed.)

Part 4

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

underestimatesunderestimates

the 2010 population by

enter your response here

million.

B.

The rounded number

overestimatesoverestimates

the 2010 population by

enter your response here

million.