   Chapter 3.7, Problem 28E ### 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 table shows how the average age of first marriage of Japanese women has varied since 1950. (a) Use a graphing calculator or computer to model these data with a fourth-degree polynomial.(b) Use part (a) to find a model for A′(t).(c) Estimate the rate of change of marriage age for women in 1990.(d) Graph the data points and the models for A and A′.

(a)

To determine

To find: To model the given data with a fourth-degree polynomial.

Explanation

Given:

The average age of first marriage of Japanese women has varied since 1950 is shown in table (1).

 t A(t) 1950 23.00 1955 23.80 1960 24.40 1965 24.50 1970 24.20 1975 24.70 1980 25.20 1985 25.50 1990 25.90 1995 26.30 2000 27.00 2005 28.00

Calculation:

Model the given data with a fourth-degree polynomial.

A(t)=at4+bt3+ct2+dt+e (1)

Plot the graph between t and A(t) using table (1) as shown in figure (1).

Refer the figure (1).

The fourth-degree polynomial for the curve is as below.

A(t)=1.2×106t4+0

(b)

To determine

To find: The model for A'(t) by using part (a).

(c)

To determine

To estimate: The rate of change of marriage age for women in 1990.

(d)

To determine

To sketch: The graph of data points and models for A and A'.

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