Question

the following table of data from a bureau of the census gives the median age of a man at the time of his first marriage.

year	1910	1920	1930	1940	1950	1960	1970	1980	1990	2000	2010
median age	25.5	24.8	24.4	24.1	22.4	22.4	23.6	24.9	26.3	26.7	27.6

a. determine the average rate of change in median age per year from 1950 to 2010
b. describe what the average rate of change in part a represents in this situation.
a. the average rate of change in median age per year from 1950 to 2010 is approximately 0.0867 years of age/yr (type an integer or a decimal. round to four decimal places as needed.)
b. choose the correct answer below
a. the median age of a man at the time of his first marriage is increasing at an average rate of years of age/yr (type an integer or a decimal. round to four decimal places as needed.)
b. the median age of a man at the time of his first marriage is decreasing at an average rate of years of age/yr (type an integer or a decimal. round to four decimal places as needed)
c. the median age of a man at the time of his first marriage remains the same.

Explanation:

Step1: Identify the years and median - ages

In 1950, the year $x_1 = 1950$ and the median - age $y_1=22.4$. In 2010, the year $x_2 = 2010$ and the median - age $y_2 = 27.6$.

Step2: Use the average rate of change formula

The formula for the average rate of change is $\frac{y_2 - y_1}{x_2 - x_1}$. Substitute $x_1 = 1950$, $y_1=22.4$, $x_2 = 2010$, and $y_2 = 27.6$ into the formula: $\frac{27.6 - 22.4}{2010 - 1950}=\frac{5.2}{60}\approx0.0867$.

Step3: Interpret the average rate of change

The positive value of the average rate of change indicates that the median age of a man at the time of his first marriage is increasing.

Answer:

a. $0.0867$
b. A. The median age of a man at the time of his first marriage is increasing at an average rate of $0.0867$ years of age/yr