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 28E
To determine

To fill: The number of book purchased in the year given in table.

Expert Solution

Answer to Problem 28E

The table shows the number of books purchased by the collector in that particular year.

Year Number of books   Year Number of books
1980 420   1995 1020
1981 460   1997 1100
1982 500   1998 1140
1985 620   1999 1180
1990 820   2000 1220
1992 900      

Explanation of Solution

The given table is,

Year Number of books   Year Number of books
1980 420   1995 __
1981 460   1997 __
1982 __   1998 __
1985 __   1999 __
1990 __   2000 1220
1992 __      

A rare book collector purchased 40 books per year between the year 1980 to 2000.

As from the given table up to year 1980 he purchased 420 books and after that he started adding 40 more books each year in his collection of rare books.

So, the formula to calculate the total number of books purchased by the rare book collector in any year is,

{Totalnumberofbookspurchasedinyearx}=Bookpurchasedinyear1980+(x1980)(40) (1)

Substitute 1982 for x in equation (1) 420 for number of books purchased in year 1980 to calculate the number of books purchased in year 1982.

Totalnumberofbookspurchasedinyear1982=420+(19821980)(40)=420+2(40)=420+80=500

Substitute 1985 for x in equation (1) 420 for number of books purchased in year 1980 to calculate the number of books purchased in year 1985.

Totalnumberofbookspurchasedinyear1985=420+(19851980)(40)=420+5(40)=420+200=620

Substitute 1990 for x in equation (1) 420 for number of books purchased in year 1980 to calculate the number of books purchased in year 1990.

Totalnumberofbookspurchasedinyear1990=420+(19901980)(40)=420+10(40)=420+400=820

Substitute 1992 for x in equation (1) 420 for number of books purchased in year 1980 to calculate the number of books purchased in year 1992.

Totalnumberofbookspurchasedinyear1992=420+(19921980)(40)=420+12(40)=420+480=900

Substitute 1995 for x in equation (1) 420 for number of books purchased in year 1980 to calculate the number of books purchased in year 1995.

Totalnumberofbookspurchasedinyear1995=420+(19951980)(40)=420+15(40)=420+600=1020

Substitute 1997 for x in equation (1) 420 for number of books purchased in year 1980 to calculate the number of books purchased in year 1997.

Totalnumberofbookspurchasedinyear1997=420+(19971980)(40)=420+17(40)=420+680=1100

Substitute 1998 for x in equation (1) 420 for number of books purchased in year 1980 to calculate the number of books purchased in year 1998.

Totalnumberofbookspurchasedinyear1998=420+(19981980)(40)=420+18(40)=420+720=1140

Substitute 1999 for x in equation (1) 420 for number of books purchased in year 1980 to calculate the number of books purchased in year 1999.

Totalnumberofbookspurchasedinyear1998=420+(19991980)(40)=420+19(40)=420+760=1180

Fill all the solutions in the given table.

Year Number of books   Year Number of books
1980 420   1995 1020
1981 460   1997 1100
1982 500   1998 1140
1985 620   1999 1180
1990 820   2000 1220
1992 900      

The table shows the number of books purchased by the collector in that particular year.

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