10
QuizMultiple Choice

Average Rate of Change

Question 10 • Applications and Modeling

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.Year1910192019301940195019601970198019902000Median Age25.124.624.324.322.822.823.224.726.126.8What does it mean in this situation if the average rate of change is negative?

Answer
A
It means that the median age of a man at the time of his first marriage is increasing.
B
It means that the median age of a man at the time of his first marriage is decreasing.
C
It means that the median age of a man at the time of his first marriage has a constant rate of change.
D
There is no way to determine the average rate of change in this situation.

Explanation

A negative average rate of change means the quantity is lower at the end of the time interval than at the beginning. Here, the quantity is the median age of a man at his first marriage, so a negative rate means that age is decreasing over the interval considered. The correct choice is “the median age of a man at the time of his first marriage is decreasing.”

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