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

### Precalculus: Mathematics for Calcu...

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

### 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

The average rate of change between 1993 and 2003 is 7.2

### Explanation of Solution

Given information:

 Year Cd player sold 1993 512 1994 520 1995 413 1996 410 1997 468 1998 510 1999 590 2000 607 2001 732 2002 612 2003 584

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

Theaverage rate of change between 1993 and 1994 is 8

### Explanation of Solution

Given information:

 Year Cd player sold 1993 512 1994 520 1995 413 1996 410 1997 468 1998 510 1999 590 2000 607 2001 732 2002 612 2003 584

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

The average rate of change between 1994 and 1996 is 55

### Explanation of Solution

Given information:

 Year Cd player sold 1993 512 1994 520 1995 413 1996 410 1997 468 1998 510 1999 590 2000 607 2001 732 2002 612 2003 584

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

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:

 Year Cd player sold 1993 512 1994 520 1995 413 1996 410 1997 468 1998 510 1999 590 2000 607 2001 732 2002 612 2003 584

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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