Chapter 1.2, Problem 1TU

TEST YOUR UNDERSTANDING|FOR EXAMPLE 1.3

Use the notion of the example. Explain the meaning of $W\left(1973\right)$, and use the average rate of change to estimate its value.

Example 1.3 WOMEN EMPLOYED OUTSIDE THE HOME

Table 1.2 shows the number $W$ of women in the United States employed outside the home as a function of the date $d$. It was taken from the Statistical Abstract of the United States

TABLE 1.2 Number of Women Employed Outside the Home in the United States

$d=Year$	$1970$	$1980$	$1990$	$2000$	$2010$
$W=Numberinmillions$	$31.5$	$45.5$	$56.8$	$66.3$	$71.9$

Part 1 Explain the meaning of $W\left(1970\right)$ and give its value.

Part 2 Explain the meaning of $W\left(1975\right)$ and estimate its value.

Part 3 Express the number of women employed outside the home in $1972$ in functional notation, and use the average yearly rate of change from $1970$ to $1980$ to estimate its value.

Part 4 According to the $1950$ Statistical Abstract of the United States, in $1943$ there were $18.7$ million women employed outside the home, and in $1946$ the number was $16.8$ million. On the basis of this information, find the average yearly rate of change in $W$ from $1943$ to $1946$ and the average decrease per year over this time interval. Use the result to estimate $W\left(1945\right)$.