   Chapter 2, Problem 52RE ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# The total fertility rate at time t, denoted by F(t), is an estimate of the average number of children born to each woman (assuming that current birth rates remain constant). The graph of the total fertility rate in the United States shows the fluctuations from 1940 to 2010.(a) Estimate the values of F'(l950), F'(l965), and F'(1987).(b) What are the meanings of these derivatives?(c) Can you suggest reasons for the values of these derivatives? (a)

To determine

To estimate: The value of F(1950),F(1965) and F(1987).

Explanation

Graph:

Calculation:

From the Figure 1, it is clear that the slope of the line AB is estimation of value F(1950).

The slope of AB is calculated as flows,

m=3.52.519551945=110=0.1

So, F(1950)0.1

Thus, the estimated value of F(1950) is 0.1.

Graph:

Calculation:

From the Figure 2, it is clear that the slope of the line AB is estimation of value F(1965).

The slope of AB is calculated as flows,

m=3.72.419601970=1

(b)

To determine

(b)To explain: The meaning of F(1950),F(1965) and F(1987).

(c)

To determine

To suggest: The reasons for the values of the derivatives in part a.

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