BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 2.6, Problem 44E

i.

To determine

The average rate of coffee house growth from 2005 to 2007 .

Expert Solution

Explanation of Solution

Given information:

The number N of locations of a coffee house chain is shown in table.

    Year20032004200520062007
    N72258569102411244015011

Calculations:

Here the growth of coffee house from 2005 to 2006 is 1244010241=2199

Here the growth of coffee house from 2006 to 2007 is 1501112440=2571

Here the average growth of coffee house from 2005 to 2007 is 2199+25712=2385

ii.

To determine

The average rate of coffee house growth from 2005 to 2006

Expert Solution

Explanation of Solution

Given information:

The number N of locations of a coffee house chain is shown in table.

    Year20032004200520062007
    N72258569102411244015011

Calculations:

Number of coffee house in 2005 is 10241 .

Number of coffee house in 2006 is 12440 .

Here the growth of coffee house from 2005 to 2006 is 1244010241=2199

iii.

To determine

The average rate of coffee house growth from 2004 to 2005

Expert Solution

Explanation of Solution

Given information:

The number N of locations of a coffee house chain is shown in table.

    Year20032004200520062007
    N72258569102411244015011

Calculations:

The number of cell phone subscribers in 2004 is 8569 .

The number of cell phone subscribers in 2005 is 10241 .

Thus the growth of cell phone users from 2004 to 2005 is 102418569=1672

iv.

To determine

The instantaneous rate of growth in 2005 by taking the average of two average rate of change.

Expert Solution

Explanation of Solution

The number N of locations of a coffee house chain is shown in table.

    Year20032004200520062007
    N72258569102411244015011

Calculations:

Thus the average number of coffee house from 2004 to 2005 is 10241+85692=9405

Therefore the instantaneous rate of growth in 2005 is 102419405=836

v.

To determine

The instantaneous rate of growth in 2005 by measuring the slope of tangent.

Expert Solution

Explanation of Solution

The number N of locations of a coffee house chain is shown in table.

    Year20032004200520062007
    N72258569102411244015011

Calculations:

The slope of the tangent is given the formula,

  f'(x)=limh0f(x+h)f(x)h

  Slope=1024185691=1672

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