Holt Mcdougal Larson Algebra 2: Student Edition 2012
Holt Mcdougal Larson Algebra 2: Student Edition 2012
1st Edition
ISBN: 9780547647159
Author: HOLT MCDOUGAL
Publisher: HOLT MCDOUGAL
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Chapter 2.7, Problem 64PS
Solution

(a.)

To Complete: The given table.

It has been determined that the value of the second deposit for year 3 is 1000g , its value for year 4 is 1000g2 and the value of the third deposit for year 4 is 1000g . These values complete the given table.

Given:

An amount of $1000 is saved and deposited into a bank account at the end of each summer, each year towards buying a used car in four years.

The growth factor 1+r , where r is the annual interest rate expressed as a decimal, is denoted by g .

The following table shows the value of the deposits over the four-year period:

  Holt Mcdougal Larson Algebra 2: Student Edition 2012, Chapter 2.7, Problem 64PS , additional homework tip  1

Concept used:

The amount after a year is given as the product of the principle (value of the deposit) at the start of the year and the growth factor.

Calculation:

The value of the second deposit for year 2 is 1000 .

The growth factor is g .

Then, the value of the second deposit for year 3 is 1000g and for year 4 is 1000g2 .

The value of the third deposit for year 3 is 1000 .

The growth factor is g .

Then, the value of the third deposit for year 4 is 1000g .

These are the required values that complete the given table.

Conclusion:

It has been determined that the value of the second deposit for year 3 is 1000g , its value for year 4 is 1000g2 and the value of the third deposit for year 4 is 1000g . These values complete the given table.

(b.)

To Write: A polynomial function that gives the value v of the account at the end of the fourth summer in terms of g .

It has been determined that a polynomial function that gives the value v of the account at the end of the fourth summer in terms of g , is v=1000g3+1000g2+1000g+1000 .

Given:

An amount of $1000 is saved and deposited into a bank account at the end of each summer, each year towards buying a used car in four years.

The growth factor 1+r , where r is the annual interest rate expressed as a decimal, is denoted by g .

The following table shows the value of the deposits over the four-year period:

  Holt Mcdougal Larson Algebra 2: Student Edition 2012, Chapter 2.7, Problem 64PS , additional homework tip  2

Concept used:

The value of the account at the end of the fourth summer is the sum of the values of all the deposits at the end of the fourth summer.

Calculation:

According to the completed table obtained in part (a), the value of the first deposit at the end of the fourth summer is 1000g3 , the value of the second deposit at the end of the fourth summer is 1000g2 , the value of the third deposit at the end of the fourth summer is 1000g , and lastly, the value of the fourth deposit at the end of the fourth summer is 1000 .

Then, the value v of the account at the end of the fourth summer in terms of g , is given as,

  v=1000g3+1000g2+1000g+1000

Conclusion:

It has been determined that a polynomial function that gives the value v of the account at the end of the fourth summer in terms of g , is v=1000g3+1000g2+1000g+1000 .

(c.)

The growth factor and the annual interest rate needed to obtain the given amount.

It has been determined that the required growth factor is approximately 1.048 and the required annual interest rate is approximately 4.8% .

Given:

An amount of $1000 is saved and deposited into a bank account at the end of each summer, each year towards buying a used car in four years.

The growth factor 1+r , where r is the annual interest rate expressed as a decimal, is denoted by g .

The following table shows the value of the deposits over the four-year period:

  Holt Mcdougal Larson Algebra 2: Student Edition 2012, Chapter 2.7, Problem 64PS , additional homework tip  3

The amount to be saved is $4300 .

Concept used:

The required growth factor and thus the required annual interest rate can be obtained by plugging in the given value of v and determining the roots of the resulting polynomial.

Calculation:

As determined previously, the value v of the account at the end of the fourth summer in terms of g , is given as,

  v=1000g3+1000g2+1000g+1000

It is given that the amount to be saved is $4300 .

Then, v=4300 .

Put v=4300 in the above polynomial function to get,

  1000g3+1000g2+1000g+1000=4300

Simplifying,

  g3+g2+g+1=4.3

On further simplification,

  g3+g2+g+14.3=0

Finally,

  g3+g2+g3.3=0

The graph of the above polynomial is given as,

  Holt Mcdougal Larson Algebra 2: Student Edition 2012, Chapter 2.7, Problem 64PS , additional homework tip  4

From the above graph, the only real root of the polynomial equation is g1.048 .

Hence, this is the required growth factor.

Now, as assumed,

  1+r=g

Put g1.048 in 1+r=g to get,

  1+r1.048

Solving,

  r0.048

This implies that the required annual interest rate is approximately 4.8% .

Conclusion:

It has been determined that the required growth factor is approximately 1.048 and the required annual interest rate is approximately 4.8% .

Chapter 2 Solutions

Holt Mcdougal Larson Algebra 2: Student Edition 2012

Ch. 2.1 - Prob. 3ECh. 2.1 - Prob. 4ECh. 2.1 - Prob. 5ECh. 2.1 - Prob. 6ECh. 2.1 - Prob. 7ECh. 2.1 - Prob. 8ECh. 2.1 - Prob. 9ECh. 2.1 - Prob. 10ECh. 2.1 - Prob. 11ECh. 2.1 - Prob. 12ECh. 2.1 - Prob. 13ECh. 2.1 - Prob. 14ECh. 2.1 - Prob. 15ECh. 2.1 - Prob. 16ECh. 2.1 - Prob. 17ECh. 2.1 - Prob. 18ECh. 2.1 - Prob. 19ECh. 2.1 - Prob. 20ECh. 2.1 - Prob. 21ECh. 2.1 - Prob. 22ECh. 2.1 - Prob. 23ECh. 2.1 - Prob. 24ECh. 2.1 - Prob. 25ECh. 2.1 - Prob. 26ECh. 2.1 - Prob. 27ECh. 2.1 - Prob. 28ECh. 2.1 - Prob. 29ECh. 2.1 - Prob. 30ECh. 2.1 - Prob. 31ECh. 2.1 - Prob. 32ECh. 2.1 - Prob. 33ECh. 2.1 - Prob. 34ECh. 2.1 - Prob. 35ECh. 2.1 - Prob. 36ECh. 2.1 - Prob. 37ECh. 2.1 - Prob. 38ECh. 2.1 - Prob. 39ECh. 2.1 - Prob. 40ECh. 2.1 - Prob. 41ECh. 2.1 - Prob. 42ECh. 2.1 - Prob. 43ECh. 2.1 - Prob. 44ECh. 2.1 - Prob. 45ECh. 2.1 - Prob. 46ECh. 2.1 - Prob. 47ECh. 2.1 - Prob. 48ECh. 2.1 - Prob. 49PSCh. 2.1 - Prob. 50PSCh. 2.1 - Prob. 51PSCh. 2.1 - Prob. 52PSCh. 2.1 - Prob. 53PSCh. 2.1 - Prob. 54PSCh. 2.1 - Prob. 1DCCh. 2.1 - 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Prob. 3ECh. 2.8 - Prob. 4ECh. 2.8 - Prob. 5ECh. 2.8 - Prob. 6ECh. 2.8 - Prob. 7ECh. 2.8 - Prob. 8ECh. 2.8 - Prob. 9ECh. 2.8 - Prob. 10ECh. 2.8 - Prob. 11ECh. 2.8 - Prob. 12ECh. 2.8 - Prob. 13ECh. 2.8 - Prob. 14ECh. 2.8 - Prob. 15ECh. 2.8 - Prob. 16ECh. 2.8 - Prob. 17ECh. 2.8 - Prob. 18ECh. 2.8 - Prob. 19ECh. 2.8 - Prob. 20ECh. 2.8 - Prob. 21ECh. 2.8 - Prob. 22ECh. 2.8 - Prob. 23ECh. 2.8 - Prob. 24ECh. 2.8 - Prob. 25ECh. 2.8 - Prob. 26ECh. 2.8 - Prob. 27ECh. 2.8 - Prob. 28ECh. 2.8 - Prob. 29ECh. 2.8 - Prob. 30ECh. 2.8 - Prob. 31ECh. 2.8 - Prob. 32ECh. 2.8 - Prob. 33ECh. 2.8 - Prob. 34ECh. 2.8 - Prob. 35ECh. 2.8 - Prob. 36ECh. 2.8 - Prob. 37ECh. 2.8 - Prob. 38ECh. 2.8 - Prob. 39PSCh. 2.8 - Prob. 40PSCh. 2.8 - Prob. 41PSCh. 2.8 - Prob. 42PSCh. 2.8 - Prob. 43PSCh. 2.8 - Prob. 44PSCh. 2.8 - Prob. 1QCh. 2.8 - Prob. 2QCh. 2.8 - Prob. 3QCh. 2.8 - Prob. 4QCh. 2.8 - Prob. 5QCh. 2.8 - Prob. 6QCh. 2.8 - Prob. 7QCh. 2.8 - Prob. 8QCh. 2.8 - Prob. 9QCh. 2.8 - Prob. 10QCh. 2.8 - Prob. 1MRPSCh. 2.8 - Prob. 2MRPSCh. 2.8 - Prob. 3MRPSCh. 2.8 - Prob. 4MRPSCh. 2.8 - Prob. 5MRPSCh. 2.8 - Prob. 6MRPSCh. 2.8 - Prob. 7MRPSCh. 2 - Prob. 1VECh. 2 - Prob. 2VECh. 2 - Prob. 3VECh. 2 - Prob. 4VECh. 2 - Prob. 5REAECh. 2 - Prob. 6REAECh. 2 - Prob. 7REAECh. 2 - Prob. 8REAECh. 2 - Prob. 9REAECh. 2 - Prob. 10REAECh. 2 - Prob. 11REAECh. 2 - Prob. 12REAECh. 2 - Prob. 13REAECh. 2 - Prob. 14REAECh. 2 - Prob. 15REAECh. 2 - Prob. 16REAECh. 2 - Prob. 17REAECh. 2 - Prob. 18REAECh. 2 - Prob. 19REAECh. 2 - Prob. 20REAECh. 2 - Prob. 21REAECh. 2 - Prob. 22REAECh. 2 - Prob. 23REAECh. 2 - Prob. 24REAECh. 2 - Prob. 25REAECh. 2 - Prob. 26REAECh. 2 - Prob. 27REAECh. 2 - Prob. 28REAECh. 2 - Prob. 29REAECh. 2 - Prob. 30REAECh. 2 - Prob. 31REAECh. 2 - Prob. 32REAECh. 2 - Prob. 33REAECh. 2 - Prob. 34REAECh. 2 - Prob. 35REAECh. 2 - Prob. 36REAECh. 2 - Prob. 37REAECh. 2 - Prob. 38REAECh. 2 - Prob. 39REAECh. 2 - Prob. 40REAECh. 2 - Prob. 1TCh. 2 - Prob. 2TCh. 2 - Prob. 3TCh. 2 - Prob. 4TCh. 2 - Prob. 5TCh. 2 - Prob. 6TCh. 2 - Prob. 7TCh. 2 - Prob. 8TCh. 2 - Prob. 9TCh. 2 - Prob. 10TCh. 2 - Prob. 11TCh. 2 - Prob. 12TCh. 2 - Prob. 13TCh. 2 - Prob. 14TCh. 2 - Prob. 15TCh. 2 - Prob. 16TCh. 2 - Prob. 17TCh. 2 - Prob. 18TCh. 2 - Prob. 19TCh. 2 - Prob. 20TCh. 2 - Prob. 21TCh. 2 - Prob. 22TCh. 2 - Prob. 23TCh. 2 - Prob. 24TCh. 2 - Prob. 25TCh. 2 - Prob. 26TCh. 2 - Prob. 27TCh. 2 - Prob. 28TCh. 2 - Prob. 29TCh. 2 - Prob. 1PCh. 2 - Prob. 2PCh. 2 - Prob. 1TPCh. 2 - Prob. 2TPCh. 2 - Prob. 3TPCh. 2 - Prob. 4TPCh. 2 - Prob. 5TPCh. 2 - Prob. 6TPCh. 2 - Prob. 7TPCh. 2 - Prob. 8TPCh. 2 - Prob. 9TPCh. 2 - Prob. 10TPCh. 2 - Prob. 11TPCh. 2 - Prob. 12TPCh. 2 - Prob. 13TPCh. 2 - Prob. 14TPCh. 2 - Prob. 15TPCh. 2 - Prob. 16TPCh. 2 - Prob. 17TPCh. 2 - Prob. 18TPCh. 2 - Prob. 19TPCh. 2 - Prob. 20TPCh. 2 - Prob. 21TP
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