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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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BuyFindarrow_forward

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.

Chapter 3.7, Problem 28E, The table shows how the average age of first marriage of Japanese women has varied since 1950. (a)

(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).

tA(t)
195023.00
195523.80
196024.40
196524.50
197024.20
197524.70
198025.20
198525.50
199025.90
199526.30
200027.00
200528.00

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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