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 43E

i.

To determine

The average rate of cell phone growth from 2002 to 2006 .

Expert Solution

Explanation of Solution

Given information:

The number N of US cell phone subscribers (in millions) is shown in table.

    t199619982000200220042006
    N4469109141182233

Calculations:

Here the growth of cell phone users from 2002 to 2004 is 182141=41

Thus the average growth of cell phone users from 2002 to 2004 is 412=20.5

Here the growth of cell phone users from 2004 to 2006 is 233182=51

Here the average growth of cell phone users from 2004 to 2006 is 512=25.5

Therefore the average rate of cell phone growth from 2002 to 2006 is 20.5+25.52=462=23

ii.

To determine

The average rate of cell phone growth from 2002 to 2004

Expert Solution

Explanation of Solution

Given information:

The number N of US cell phone subscribers (in millions) is shown in table.

    t199619982000200220042006
    N4469109141182233

Calculations:

The number of cell phone subscribers in 2002 is 141 .

The number of cell phone subscribers in 2004 is 182 .

Thus the growth of cell phone users from 2002 to 2004 is 182141=41

Thus the average growth of cell phone users from 2002 to 2004 is 412=20.5

iii.

To determine

The average rate of cell phone growth from 2000 to 2002

Expert Solution

Explanation of Solution

Given information:

The number N of US cell phone subscribers (in millions) is shown in table.

    t199619982000200220042006
    N4469109141182233

Calculations:

The number of cell phone subscribers in 2000 is 109 .

The number of cell phone subscribers in 2002 is 141 .

Thus the growth of cell phone users from 2000 to 2002 is 141109=32

Thus the average growth of cell phone users from 2000 to 2002 is 322=16

iv.

To determine

The instantaneous rate of growth in 2002 by taking the average of two average rate of change.

Expert Solution

Explanation of Solution

Given information:

The number N of US cell phone subscribers (in millions) is shown in table.

    t199619982000200220042006
    N4469109141182233

Calculations:

Thus the average growth of cell phone users from 2000 to 2002 is 322=16

Therefore the instantaneous rate of growth in 2002 is 141(109+16)=16

v.

To determine

The instantaneous rate of growth in 2002 by measuring the slope of tangent.

Expert Solution

Explanation of Solution

Given information:

The number N of US cell phone subscribers (in millions) is shown in table.

    t199619982000200220042006
    N4469109141182233

Calculations:

Thus the average growth of cell phone users from 2000 to 2002 is 322=16

The slope of the tangent is given the formula,

  f'(x)=limh0f(x+h)f(x)h

  Slope=141(109+16)1=16

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