Question

Age in the United States The median age of the U.S.

population for each year t between 1970 and 2010 can
be approximated by A(t) = 0.2431 - 450.8.
(Source: U.S. Census Bureau.)
(a) Compute the dian ages in 1980 and 2000.
(b) What is the slope of the graph of A? Interpret the slope

Answer 1

a)In year 1980, the median age is 30.54.

In year, 2000 the median age is 35.4

b) The slope is 0.2431

It indicates the average annual change in the median age of the U.S. population.

How to calculate median age using line equation

Given

A(t) = 0.2431t - 450.8

Where

median age(A) is a function of year,t

(a) Computing the median ages in 1980 and 2000 involves substituting for t

For t = 1980,

A(1980) = 0.2431(1980) - 450.8

= 481.34 - 450.8

= 30.54

In year 1980, the median age is 30.54.

For t = 2000,

A(2000) = 0.2431(2000) - 450.8

= 486.2 - 450.8

= 35.4

In year, 2000 the median age is 35.4

(b) The slope is the coefficient of t in the function. The slope = 0.2431

The slope represents the rate at which the median age is changing with respect to time. So, it indicates the average annual change in the median age of the U.S. population.