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CalculusCalculus: An Applied Approach (MindTap Course List)10th Edition

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Chapter 7.2, Problem 51E
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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Modeling Data Personal consumption expenditures (in billions of dollars) for several types of recreation from 2008 through 2013 are shown in the table, where a is the expenditures on amusement parks and campgrounds, y is the expenditures on live entertainment (excluding sports), and z is the expenditures on spectator sports.

Year 2008 2009 2010 2011 2012 2013
X 38.3 37.2 38.8 41.3 44.4 46.5
y 24.3 25.2 26.3 28.3 28.4 28.7
z 19.4 18.8 19.2 20.4 21.2 22.3

Spreadsheet at LarsonAppliedCalculus.com

A model for the data in the table is given by

− 0.391 x + 0.069 x +   z   = 6.

(Source: U.S. Bureau of Economic Analysis)

(a) Add a fifth row to the table using the model to approximate z for the given values of x and y. Compare the approximations with the actual values of z.

(b) According to this model, increases in expenditures of recreation types y and z would correspond to what kind of change in expenditures of recreation type x?

(a)

To determine

To calculate: The fifth row with the help of model to approximate z for the provided values of x and y and then compare the approximate value to the actual values of z.

Explanation

Given information:

There are personal consumption expenditure from 2008 to 2013in which many type of recreation are shown in the table.

The provided table is

Year 2008 2009 2010 2011 2012 2013
x 38.3 37.2 38.8 41.3 44.4 46.5
y 24.3 25.2 26.3 28.3 28.4 28.7
z 19.4 18.8 19.2 20.4 21.2 22.3

The provided model equation for the data is −0.391x+0.069y+z=6.

Here, x is the expenditures on amusement park and campgrounds, y is the expenditures on live entertainment and z is the expenditures on spectators sports.

Calculation:

Consider the provided equation, −0.391x+0.069y+z=6

The approximate value of z can be found out by putting the values of x and y which is provided in the table in the above equation.

For 2008, put the value of x=38.3 and y=24.3 in the above equation.

−0.391x+0.069y+z=6−0.391⋅(38.3)+0.069⋅(24.3)+z=6−14.9753+1.6767+z=6z=6+14.9753−1.6767

On further simplification,

z=6+14.9753−1.6767z=19.2986z≈19.3

For 2009, put the value of x=37.2 and y=25.2 in the above equation.

−0.391x+0.069y+z=6−0.391⋅(37.2)+0.069⋅(25.2)+z=6−14.5452+1.7388+z=6z=6+14.5452−1.7388

On further simplification,

z=6+14.5452−1.7388z=18.8064z≈18.8

For 2010, put the value of x=38.8 and y=26.3 in the above equation.

−0.391x+0.069y+z=6−0.391⋅(38.8)+0.069⋅(26.3)+z=6−15.1708+1.8147+z=6z=6+15.1702−1.8147

On further simplification,

z=6+15

(b)

To determine

The change in expenditures of recreation type x if increases in expenditures of recreation type y and z.

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Sect-7.1 P-1CPSect-7.1 P-2CPSect-7.1 P-3CPSect-7.1 P-4CPSect-7.1 P-5CPSect-7.1 P-6CPSect-7.1 P-7CPSect-7.1 P-1SWUSect-7.1 P-2SWUSect-7.1 P-3SWU
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Radical Expressions Evaluate the radical expression, and express the result in the form a + bi. 60. 3629

Precalculus: Mathematics for Calculus (Standalone Book)

Determine whether the series converges or diverges. 21.n=11+n2+n

Calculus: Early Transcendentals

A particle moves along a straight line with equation of motions s = f(t), where s is measured in meters and t i...

Single Variable Calculus: Early Transcendentals, Volume I

Solve the following problems. a. Find the mean, median, and mode for the scores in the following frequency dist...

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

CJ The local police force gives all applicants an entrance exam and accepts only those applicants who score in ...

Essentials Of Statistics

In Exercises 1-8, use the graph of the given function f to determine limxaf(x) at the indicated value of a, if ...

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Find da parametric representation for the surface. The part of the sphere x2+y2+z2=36 that lies between the pla...

Calculus (MindTap Course List)

For Problems 15-20, use the specified number of classes to do the following. (a) Find the class width. (b) Make...

Understanding Basic Statistics

Use a stem and leaf display to organize the following distribution of scores. Use six stems with each stem corr...

Statistics for The Behavioral Sciences (MindTap Course List)

Show that the function f(x)={x4sin(1/x)ifx00ifx=0 is continuous on (,).

Single Variable Calculus

In Problems 7-34, perform the indicated operations and simplify. 19.

Mathematical Applications for the Management, Life, and Social Sciences

In each of the following, determine the nth-term formula for the number of square tiles in the nth figure.

Mathematical Excursions (MindTap Course List)

Suppose Appendix Table A.3 contained (z) only for z 0. Explain how you could still compute a. P(1.72 Z .55) ...

Probability and Statistics for Engineering and the Sciences

Solve each equation in Exercises 107120 for x, rounding your answer to four significant digits where necessary....

Finite Mathematics

For Problems 5-54, perform the following operations with real numbers. Objectives 3-6 -17-9

Intermediate Algebra

What is wrong with the equation? 21x4dx=x33]21=38

Single Variable Calculus: Early Transcendentals

Find all six trigonometric functions of if the given point is on the terminal side of . (In Problem 15, assume...

Trigonometry (MindTap Course List)

Given P=2(l+w), where l=418 in. and w=234 in., find P.

Elementary Technical Mathematics

Write the formula for calculating an amortization payment by table. (12-8)

Contemporary Mathematics for Business & Consumers

5. Prove that contain a zero divisor if and only if does.

Elements Of Modern Algebra

Points A and B have symmetry with respect to the y-axis. Find the coordinates of A if B is the point: a 3,-4 c ...

Elementary Geometry For College Students, 7e

Graphical Reasoning The graph of the first derivative of a function f on the interval 7,5 is shown. Use the g...

Calculus of a Single Variable

Testing for Continuity In Exercises 75-82, describe the interval(s) on which the function is continuous. f(x)=c...

Calculus: Early Transcendental Functions (MindTap Course List)

For Review Exercises 7 to 11 use the given information to name the segments that must be parallel. If there are...

Elementary Geometry for College Students

The odds in favor of an event E occurring are 9 to 7. What is the probability of E occurring?

Finite Mathematics for the Managerial, Life, and Social Sciences

True or False: is a convergent series.

Study Guide for Stewart's Multivariable Calculus, 8th

Finding an Indefinite Integral In Exercises 91-108, find the indefinite integral. exexex+exdx

Calculus

Verifying a Property Use a graph to explain why abkf(x)dx=kabf(x)dx if f is integrable on [a, b] and k is a con...

Calculus (MindTap Course List)

A population of ants on an island is modeled by , where t is the number of years since 1970. How long did it ta...

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Finding a Particular Solution In Exercises 9-12, find the particular solution of the differential equation that...

Multivariable Calculus

Consider the chance experiment described in the previous exercise. a. What is the estimated probability that a ...

Introduction To Statistics And Data Analysis

Find dimension x. All dimensions are in millimeters

Mathematics For Machine Technology

Ward Doering Auto Sales is considering offering a special service contract that will coverthe total cost of any...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

A client wants to determine whether there is a significant difference in the time required to complete a progra...

Statistics for Business & Economics, Revised (MindTap Course List)

Describe the circumstances in which counterbalancing is used and explain what it is trying to accomplish.

Research Methods for the Behavioral Sciences (MindTap Course List)

Find the probability of drawing a black card or a king on one draw from a card deck.

College Algebra (MindTap Course List)

Answer the following questions using complete sentences and your own words. HANDS ON Suppose you had a baby in...

Mathematics: A Practical Odyssey

Suppose that you wake up in the morning with all the symptoms of a head cold. You take a cold pill and eat a bi...

Research Methods for the Behavioral Sciences (MindTap Course List)

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