BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 2.4, Problem 27E

a

To determine

To find the average rate of change of sales between 1993 and 2003.

Expert Solution

Answer to Problem 27E

The average rate of change between 1993 and 2003 is 7.2

Explanation of Solution

Given information:

    YearCd player sold
    1993512
    1994520
    1995413
    1996410
    1997468
    1998510
    1999590
    2000607
    2001732
    2002612
    2003584

Formula used:

The average rate of change of the function y=f(x) between x=a and x=b is

  change in ychange in zf(b)f(a)ba      

Calculation:

Therefore the average rate of change between 1993 and 2003 is

  =CD2003CD199320031993=58451210=7210=7.2    

Hence, the average rate of change between 1993 and 2003 is 7.2

b

To determine

To find the average rate of change of sales between 1993 and 1994.

Expert Solution

Answer to Problem 27E

Theaverage rate of change between 1993 and 1994 is 8

Explanation of Solution

Given information:

    YearCd player sold
    1993512
    1994520
    1995413
    1996410
    1997468
    1998510
    1999590
    2000607
    2001732
    2002612
    2003584

Formula used:

The average rate of change of the function y=f(x) between x=a and x=b is

  change in ychange in zf(b)f(a)ba      

Calculation:

Therefore the average rate of change between 1993 and 1994 is

  =CD1994CD199319941993=5205121=8

Hence, the average rate of change between 1993 and 1994 is 8

c

To determine

To find the average rate of change of sales between 1994 and 1996.

Expert Solution

Answer to Problem 27E

The average rate of change between 1994 and 1996 is 55

Explanation of Solution

Given information:

    YearCd player sold
    1993512
    1994520
    1995413
    1996410
    1997468
    1998510
    1999590
    2000607
    2001732
    2002612
    2003584

Formula used:

The average rate of change of the function y=f(x) between x=a and x=b is

  change in ychange in zf(b)f(a)ba      

Calculation:

Therefore the average rate of change between 1994 and 1996 is

  =CD1996CD199619961994=4105202               [substitute the value]=1102                      [subtract]=55                            [divide]

Hence, the average rate of change between 1994 and 1996 is 55

d

To determine

To find the two successive year in which CD player sales increase and decrease most quickly

Expert Solution

Answer to Problem 27E

The most increase between two successive years is between 2000-2001.

The most decease between two successive years is between 2001-2002

Explanation of Solution

Given information:

    YearCd player sold
    1993512
    1994520
    1995413
    1996410
    1997468
    1998510
    1999590
    2000607
    2001732
    2002612
    2003584

Formula used:

The average rate of change of the function y=f(x) between x=a and x=b is

  change in ychange in zf(b)f(a)ba      

Calculation:

Therefore the average rate of change between 1994 and 1995 is

  =CD1995CD199419951994=4135201               [substitute the value]=107                      [subtract]

The average rate of change between 1995 and 1996 is

  =CD1996CD199519961995=4104131               [substitute the value]=3                     [subtract]

The average rate of change between 1996 and 1997 is

  =CD1997CD199619951994=4684101               [substitute the value]=58                      [subtract]

The average rate of change between 1997 and 1998 is

  =CD1998CD199719981997=5104681               [substitute the value]=48                            [subtract]

The average rate of change between 1998 and 1999 is

  =CD1999CD199819991998=5905101               [substitute the value]=80                      [subtract]

The average rate of change between 1999 and 2000 is

  =CD2000CD199920001999=6075901               [substitute the value]=17                      [subtract]

The average rate of change between 2000 and 2001 is

  =CD2001CD200020012000=7326071               [substitute the value]=25                     [subtract]

The average rate of change between 2001 and 2002 is

  =CD2002CD200119951994=6127321               [substitute the value]=120                      [subtract]

Therefore the average rate of change between 2002 and 2003 is

  =CD2003CD200220032002=5846121               [substitute the value]=28                     [subtract]

Hence,the most increase between two successive years is between 2000-2001 and

the most decease between two successive years is between 2001-2002

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