   Chapter 8.4, Problem 69E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Transportation Workers The number W (in thousands) of scenic and sightseeing transportation workers employed in the United States during 2014 can be modeled by W =31 .184 + 8 .447 sin ( 0 .568t - 2 .595 ) where t is the time (in months), with t = 1 corresponding to January. Approximate the month t in which the number of scenic and sightseeing transportation workers employed was a maximum. What was the maximum number of scenic and sightseeing transportation workers employed? (Source: U.S. Bureau of Labor Statistics)

To determine

To calculate: The maximum number of scenic and sightseeing transportation workers employed from the provided function W=31.184+8.447sin(0.568t2.595), where t is the time in months and t=1 means January.

Explanation

Given Information:

The number of scenic and sightseeing transportation workers employed is given by,

W=31.184+8.447sin(0.568t2.595)

Where t is the time in months.

Formula used:

Sine differentiation rule:

ddx[sinu]=cosududx

General power rule of differentiation:

ddx[xn]=nxn1

Calculation:

Consider the provided function:

W=31.184+8.447sin(0.568t2.595)

Differentiate the above function using Sine and general power rules of differentiation.

W=ddt[31.184]+ddt[8.447sin(0.568t2.595)]=0+((8.447cos(0.568t2.595))(0.568))=4.797cos(0.568t2.595)

Thus,

W=4.797cos(0.568t2

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