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

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Chapter 4, Problem 117RE
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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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Music The numbers of music albums downloaded D (in millions) from 2005 through 2013 can be modeled by

D =   −   179.8   +   116.84  ln t where t = 5 corresponds to 2005. Find the rates of change of the number of music albums downloaded in 2010 and 2012. (Source: Recording Industry Association of America)

To determine

To calculate: The rate of change of number of music albums that are downloaded in the year 2010 and 2012 using the model D=−179.8+116.84lnt defined for number of music albums D that are downloaded in millions from t=5 corresponds to 2005 through 2013.

Explanation

Given Information:

The model D=−179.8+116.84lnt defined for number of music albums D that are downloaded in millions from t=5 corresponds to 2005 through 2013.

Formula used:

If the function is y=[logxt], then the chain rule for logarithmic function is given by.

y′=(1lnx)⋅1t.dtdx

Constant multiple rule is ddxk⋅g(x)=kg′(x) where k is a constant.

Calculation:

Consider the model, D=−179.8+116.84lnt

Evaluate the rate of change of number of music files by determining the derivative of the function.

D′=ddt(−179.8+116.84lnt)

Evaluate the derivative by applying sum rule and constant multiple rule

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Sect-4.1 P-1CPSect-4.1 P-2CPSect-4.1 P-3CPSect-4.1 P-4CPSect-4.1 P-5CPSect-4.1 P-1SWUSect-4.1 P-2SWUSect-4.1 P-3SWUSect-4.1 P-4SWUSect-4.1 P-5SWU
Sect-4.1 P-6SWUSect-4.1 P-7SWUSect-4.1 P-8SWUSect-4.1 P-9SWUSect-4.1 P-10SWUSect-4.1 P-11SWUSect-4.1 P-12SWUSect-4.1 P-13SWUSect-4.1 P-14SWUSect-4.1 P-15SWUSect-4.1 P-16SWUSect-4.1 P-17SWUSect-4.1 P-18SWUSect-4.1 P-1ESect-4.1 P-2ESect-4.1 P-3ESect-4.1 P-4ESect-4.1 P-5ESect-4.1 P-6ESect-4.1 P-7ESect-4.1 P-8ESect-4.1 P-9ESect-4.1 P-10ESect-4.1 P-11ESect-4.1 P-12ESect-4.1 P-13ESect-4.1 P-14ESect-4.1 P-15ESect-4.1 P-16ESect-4.1 P-17ESect-4.1 P-18ESect-4.1 P-19ESect-4.1 P-20ESect-4.1 P-21ESect-4.1 P-22ESect-4.1 P-23ESect-4.1 P-24ESect-4.1 P-25ESect-4.1 P-26ESect-4.1 P-27ESect-4.2 P-1CPSect-4.2 P-2CPSect-4.2 P-3CPSect-4.2 P-4CPSect-4.2 P-5CPSect-4.2 P-1SWUSect-4.2 P-2SWUSect-4.2 P-3SWUSect-4.2 P-4SWUSect-4.2 P-5SWUSect-4.2 P-6SWUSect-4.2 P-7SWUSect-4.2 P-8SWUSect-4.2 P-9SWUSect-4.2 P-10SWUSect-4.2 P-11SWUSect-4.2 P-12SWUSect-4.2 P-1ESect-4.2 P-2ESect-4.2 P-3ESect-4.2 P-4ESect-4.2 P-5ESect-4.2 P-6ESect-4.2 P-7ESect-4.2 P-8ESect-4.2 P-9ESect-4.2 P-10ESect-4.2 P-11ESect-4.2 P-12ESect-4.2 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In Exercises 1536, solve the system of linear equations, using the Gauss-Jordan elimination method. 3x2y=5x+3y=...

Finite Mathematics for the Managerial, Life, and Social Sciences

Describe the auxiliary line segment as determined, overdetermined, or underdetermined. a) Through vertex B of A...

Elementary Geometry for College Students

By definition the improper integral It is not an improper integral.

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

Finding Parametric and Symmetric Equations In Exercises 37 and 38, find sets of (a) parametric equations and (b...

Multivariable Calculus

Approximating a Derivative In Exercises 67 and 68, evaluate f (2) and f (2.1) and use the results to approximat...

Calculus (MindTap Course List)

A can buoy is to be made of three pieces, namely, a cylinder and two equal cones, the altitude of each cone bei...

Calculus

The area of the parallelogram at the right is: 26

Study Guide for Stewart's Multivariable Calculus, 8th

In addition to the key words, you should also be able to define the following terms: Within-subjects design Rep...

Research Methods for the Behavioral Sciences (MindTap Course List)

A company uses three different assembly linesA1, A2 and A3to manufacture a particular component. Of those manuf...

Introduction To Statistics And Data Analysis

Define field studies and simulation, explain why they are used as alternatives to laboratory experiments, and i...

Research Methods for the Behavioral Sciences (MindTap Course List)

Given the number of cuts, the length of cut, the revolutions per minute of the workpiece or tool, and the tool ...

Mathematics For Machine Technology

You are on a TV show. You have been asked to either play a dice game five times or accept a 50 bill. The dice g...

Mathematics: A Practical Odyssey

Fill in the blanks. The polynomial function P(x)=7x4+5x32x+1 can have at most _________ positive zeros.

College Algebra (MindTap Course List)

A survey of commercial buildings served by the Cincinnati Gas Electric Company asked what main heating fuel wa...

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

Suppose that we have a sample space S = {E1, E2, E3, E4, E5, E6, E7}, where E1, E2, , E7 denote the sample poi...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

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