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Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516

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Chapter
Section
BuyFindarrow_forward

Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516
Textbook Problem

Modeling Data Outlays for national defense D (in billions of dollars) for 2006 through 2014 are shown in the table, where t is the time in years, with t = 6 corresponding to2006. (Source: U.S. Office of Management and Budget)

T 6 7 8 9 10
D 521.8 551.3 616.1 661.0 693.5
t 11 12 13 14
D 705.6 677.9 633.4 603.5

(a) Use the regression capabilities of a graphing utility to find a model of the form

D = a t 4 + b t 3 + c t 2 + d t + e

for the data.

(b) Use a graphing utility to plot the data and graph the model.

(c) For the years shown in the table, when does the model indicate that the outlay for national defense was at a

(d) For the years shown in the table, when does the model indicate that the outlay for national defense was increasing at the greatest rate?

(a)

To determine

To calculate: The fourth order polynomial model that fits the data.

Explanation

Given:

The data set where D represents the amount spent on national defence in billions of dollars and t represents the time where 6 represents 2006.

t

6

7

8

9

10

11

12

13

14

D

521.8

551.3

616.1

661

693.5

705.6

677.9

633.4

603.5

Calculation:

The model can be obtained using the Ti-83 calculator. Proceed as follows:

Step 1: Press the [STAT] key and then 1...

(b)

To determine

To graph: The function and the data points on the same coordinate axes.

(c)

To determine

To calculate: The year when the national defence spending was maximum and minimum.

(d)

To determine

To calculate: The year when the national defence spending was increasing at the highest rate.

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