   Chapter 8.4, Problem 70E ### 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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# Employment The number W (in thousands) of golf course and country club workers employed in the United States during 2014 can be modeled by W = 362 .909 + 112 .127 sin ( 0 .549t - 2 .380 ) where t is the time (in months), with t = 1 corresponding to January. Approximate the month t in which the number of golf course and country club workers employed was a maximum. What was the maximum number of golf course and country club workers employed? (Source: U.S. Bureau of Labor Statistics)

To determine

To calculate: The maximum number of golf course and country club workers employed from the provided function W=362.909+112.127sin(0.549t2.380), where t is the time in months and t=1 means January.

Explanation

Given Information:

The number of golf course and country club workers employed is given by,

W=362.909+112.127sin(0.549t2.380)

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=362.909+112.127sin(0.549t2.380)

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

W=ddt[362.909]+ddt[112.127sin(0.549t2.380)]=0+((112.127cos(0.549t2.380))(0.549))=61.55cos(0.549t2.380)

Thus,

W=61.55cos(0.549t2.380)

Now, substitute W=0 to find the value of t

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