Question

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

Answer 1

A. 0.0825 years of age per year

Answer 2

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.