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Has the marrying age of a man changed over the years? The United States Bureau of the Census takes a formal count of everyone in the U.S. every 10 years and has provided the following data that gives the median age of an American man at the time of his first marriage.


Year

1910

1920

1930

1940

1950

1960

1970

1980

1990

2000

Median Age

25.1

24.6

24.3

24.3

22.8

22.8

23.2

24.7

26.1

26.8


Determine the average rate of change in median age per year from 1950 to 1990.

a.

0.0825 years of age per year

b.

0.825 years of age per year

c.

1.21 years of age per year

d.

-1.21 years of age per year

Verified Answer :

A0.0825 years of age per year

Answer: a.  0.0825 years of age per year

Step-by-step explanation:

From the given table , the median age per year in 1950 = 22.8

The median age per year in 1990 = 26.1

We know that the average rate of change of a function f(x) from x=a to x=b is given by :-

\(\dfrac{f(b)-f(a)}{b-a}\)

Now, the the average rate of change in median age per year from 1950 to 1990 is given by :_

\(\dfrac{26.1-22.8}{1990-1950}=0.0825\)

Hence, the average rate of change in median age per year from 1950 to 1990 is 0.0825 years of age per year.