(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:

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:

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:

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+1−4.3=0

Finally,

g3+g2+g−3.3=0

The graph of the above polynomial is given as,

From the above graph, the only real root of the polynomial equation is g≈1.048 .

Hence, this is the required growth factor.

Now, as assumed,

1+r=g

Put g≈1.048 in 1+r=g to get,

1+r≈1.048

Solving,

r≈0.048

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 2.7, Problem 63PS

Chapter 2.7, Problem 65PS

Chapter 2 Solutions

Holt Mcdougal Larson Algebra 2: Student Edition 2012

Ch. 2.1 - Prob. 1GP Ch. 2.1 - Prob. 2GP Ch. 2.1 - Prob. 3GP Ch. 2.1 - Prob. 4GP Ch. 2.1 - Prob. 5GP Ch. 2.1 - Prob. 6GP Ch. 2.1 - Prob. 7GP Ch. 2.1 - Prob. 8GP Ch. 2.1 - Prob. 1E Ch. 2.1 - Prob. 2E

Ch. 2.1 - Prob. 3E Ch. 2.1 - Prob. 4E Ch. 2.1 - Prob. 5E Ch. 2.1 - Prob. 6E Ch. 2.1 - Prob. 7E Ch. 2.1 - Prob. 8E Ch. 2.1 - Prob. 9E Ch. 2.1 - Prob. 10E Ch. 2.1 - Prob. 11E Ch. 2.1 - Prob. 12E Ch. 2.1 - Prob. 13E Ch. 2.1 - Prob. 14E Ch. 2.1 - Prob. 15E Ch. 2.1 - Prob. 16E Ch. 2.1 - Prob. 17E Ch. 2.1 - Prob. 18E Ch. 2.1 - Prob. 19E Ch. 2.1 - Prob. 20E Ch. 2.1 - Prob. 21E Ch. 2.1 - Prob. 22E Ch. 2.1 - Prob. 23E Ch. 2.1 - Prob. 24E Ch. 2.1 - Prob. 25E Ch. 2.1 - Prob. 26E Ch. 2.1 - Prob. 27E Ch. 2.1 - Prob. 28E Ch. 2.1 - Prob. 29E Ch. 2.1 - Prob. 30E Ch. 2.1 - Prob. 31E Ch. 2.1 - Prob. 32E Ch. 2.1 - Prob. 33E Ch. 2.1 - Prob. 34E Ch. 2.1 - Prob. 35E Ch. 2.1 - Prob. 36E Ch. 2.1 - Prob. 37E Ch. 2.1 - Prob. 38E Ch. 2.1 - Prob. 39E Ch. 2.1 - Prob. 40E Ch. 2.1 - Prob. 41E Ch. 2.1 - Prob. 42E Ch. 2.1 - Prob. 43E Ch. 2.1 - Prob. 44E Ch. 2.1 - Prob. 45E Ch. 2.1 - Prob. 46E Ch. 2.1 - Prob. 47E Ch. 2.1 - Prob. 48E Ch. 2.1 - Prob. 49PS Ch. 2.1 - Prob. 50PS Ch. 2.1 - Prob. 51PS Ch. 2.1 - Prob. 52PS Ch. 2.1 - Prob. 53PS Ch. 2.1 - Prob. 54PS Ch. 2.1 - Prob. 1DC Ch. 2.1 - Prob. 2DC Ch. 2.1 - Prob. 3DC Ch. 2.1 - Prob. 4DC Ch. 2.1 - Prob. 5DC Ch. 2.1 - Prob. 6DC Ch. 2.2 - Prob. 1GP Ch. 2.2 - Prob. 2GP Ch. 2.2 - Prob. 3GP Ch. 2.2 - Prob. 4GP Ch. 2.2 - Prob. 5GP Ch. 2.2 - Prob. 6GP Ch. 2.2 - Prob. 7GP Ch. 2.2 - Prob. 8GP Ch. 2.2 - Prob. 9GP Ch. 2.2 - Prob. 10GP Ch. 2.2 - Prob. 11GP Ch. 2.2 - Prob. 12GP Ch. 2.2 - Prob. 1E Ch. 2.2 - Prob. 2E Ch. 2.2 - Prob. 3E Ch. 2.2 - Prob. 4E Ch. 2.2 - Prob. 5E Ch. 2.2 - Prob. 6E Ch. 2.2 - Prob. 7E Ch. 2.2 - Prob. 8E Ch. 2.2 - Prob. 9E Ch. 2.2 - Prob. 10E Ch. 2.2 - Prob. 11E Ch. 2.2 - Prob. 12E Ch. 2.2 - Prob. 13E Ch. 2.2 - Prob. 14E Ch. 2.2 - Prob. 15E Ch. 2.2 - Prob. 16E Ch. 2.2 - Prob. 17E Ch. 2.2 - Prob. 18E Ch. 2.2 - Prob. 19E Ch. 2.2 - Prob. 20E Ch. 2.2 - Prob. 21E Ch. 2.2 - Prob. 22E Ch. 2.2 - Prob. 23E Ch. 2.2 - Prob. 24E Ch. 2.2 - Prob. 25E Ch. 2.2 - Prob. 26E Ch. 2.2 - Prob. 27E Ch. 2.2 - Prob. 28E Ch. 2.2 - Prob. 29E Ch. 2.2 - Prob. 30E Ch. 2.2 - Prob. 31E Ch. 2.2 - 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Prob. 3P Ch. 2.4 - Prob. 4P Ch. 2.4 - Prob. 5P Ch. 2.4 - Prob. 6P Ch. 2.4 - Prob. 7P Ch. 2.4 - Prob. 8P Ch. 2.4 - Prob. 9P Ch. 2.4 - Prob. 10P Ch. 2.5 - Prob. 1GP Ch. 2.5 - Prob. 2GP Ch. 2.5 - Prob. 3GP Ch. 2.5 - Prob. 4GP Ch. 2.5 - Prob. 5GP Ch. 2.5 - Prob. 6GP Ch. 2.5 - Prob. 7GP Ch. 2.5 - Prob. 8GP Ch. 2.5 - Prob. 9GP Ch. 2.5 - Prob. 1E Ch. 2.5 - Prob. 2E Ch. 2.5 - Prob. 3E Ch. 2.5 - Prob. 4E Ch. 2.5 - Prob. 5E Ch. 2.5 - Prob. 6E Ch. 2.5 - Prob. 7E Ch. 2.5 - Prob. 8E Ch. 2.5 - Prob. 9E Ch. 2.5 - Prob. 10E Ch. 2.5 - Prob. 11E Ch. 2.5 - Prob. 12E Ch. 2.5 - Prob. 13E Ch. 2.5 - Prob. 14E Ch. 2.5 - Prob. 15E Ch. 2.5 - Prob. 16E Ch. 2.5 - Prob. 17E Ch. 2.5 - Prob. 18E Ch. 2.5 - Prob. 19E Ch. 2.5 - Prob. 20E Ch. 2.5 - Prob. 21E Ch. 2.5 - Prob. 22E Ch. 2.5 - Prob. 23E Ch. 2.5 - Prob. 24E Ch. 2.5 - Prob. 25E Ch. 2.5 - Prob. 26E Ch. 2.5 - Prob. 27E Ch. 2.5 - Prob. 28E Ch. 2.5 - Prob. 29E Ch. 2.5 - Prob. 30E Ch. 2.5 - Prob. 31E Ch. 2.5 - Prob. 32E Ch. 2.5 - Prob. 33E Ch. 2.5 - Prob. 34E Ch. 2.5 - Prob. 35E Ch. 2.5 - Prob. 36E Ch. 2.5 - Prob. 37E Ch. 2.5 - Prob. 38E Ch. 2.5 - Prob. 39E Ch. 2.5 - Prob. 40E Ch. 2.5 - Prob. 41PS Ch. 2.5 - Prob. 42PS Ch. 2.5 - Prob. 43PS Ch. 2.5 - Prob. 44PS Ch. 2.5 - Prob. 45PS Ch. 2.5 - Prob. 46PS Ch. 2.5 - Prob. 1MRPS Ch. 2.5 - Prob. 2MRPS Ch. 2.5 - Prob. 3MRPS Ch. 2.5 - Prob. 4MRPS Ch. 2.5 - Prob. 5MRPS Ch. 2.5 - Prob. 6MRPS Ch. 2.5 - Prob. 7MRPS Ch. 2.6 - Prob. 1GP Ch. 2.6 - Prob. 2GP Ch. 2.6 - Prob. 3GP Ch. 2.6 - Prob. 4GP Ch. 2.6 - Prob. 5GP Ch. 2.6 - Prob. 6GP Ch. 2.6 - Prob. 7GP Ch. 2.6 - Prob. 1E Ch. 2.6 - Prob. 2E Ch. 2.6 - Prob. 3E Ch. 2.6 - Prob. 4E Ch. 2.6 - Prob. 5E Ch. 2.6 - Prob. 6E Ch. 2.6 - Prob. 7E Ch. 2.6 - Prob. 8E Ch. 2.6 - Prob. 9E Ch. 2.6 - Prob. 10E Ch. 2.6 - Prob. 11E Ch. 2.6 - Prob. 12E Ch. 2.6 - Prob. 13E Ch. 2.6 - Prob. 14E Ch. 2.6 - Prob. 15E Ch. 2.6 - Prob. 16E Ch. 2.6 - Prob. 17E Ch. 2.6 - Prob. 18E Ch. 2.6 - Prob. 19E Ch. 2.6 - Prob. 20E Ch. 2.6 - Prob. 21E Ch. 2.6 - Prob. 22E Ch. 2.6 - Prob. 23E Ch. 2.6 - Prob. 24E Ch. 2.6 - Prob. 25E Ch. 2.6 - Prob. 26E Ch. 2.6 - Prob. 27E Ch. 2.6 - Prob. 28E Ch. 2.6 - Prob. 29E Ch. 2.6 - Prob. 30E Ch. 2.6 - Prob. 31E Ch. 2.6 - Prob. 32E Ch. 2.6 - Prob. 33E Ch. 2.6 - Prob. 34E Ch. 2.6 - Prob. 35E Ch. 2.6 - Prob. 36E Ch. 2.6 - Prob. 37E Ch. 2.6 - Prob. 38E Ch. 2.6 - Prob. 39E Ch. 2.6 - Prob. 40E Ch. 2.6 - Prob. 41E Ch. 2.6 - Prob. 42E Ch. 2.6 - Prob. 43E Ch. 2.6 - Prob. 44E Ch. 2.6 - Prob. 45PS Ch. 2.6 - Prob. 46PS Ch. 2.6 - Prob. 47PS Ch. 2.6 - Prob. 48PS Ch. 2.6 - Prob. 49PS Ch. 2.6 - Prob. 50PS Ch. 2.6 - Prob. 51PS Ch. 2.6 - Prob. 1Q Ch. 2.6 - Prob. 2Q Ch. 2.6 - Prob. 3Q Ch. 2.6 - Prob. 4Q Ch. 2.6 - Prob. 5Q Ch. 2.6 - Prob. 6Q Ch. 2.6 - Prob. 7Q Ch. 2.6 - Prob. 8Q Ch. 2.6 - Prob. 9Q Ch. 2.6 - Prob. 10Q Ch. 2.6 - Prob. 11Q Ch. 2.6 - Prob. 12Q Ch. 2.6 - Prob. 13Q Ch. 2.6 - Prob. 1P Ch. 2.6 - Prob. 2P Ch. 2.6 - Prob. 3P Ch. 2.6 - Prob. 4P Ch. 2.7 - Prob. 1GP Ch. 2.7 - Prob. 2GP Ch. 2.7 - Prob. 3GP Ch. 2.7 - Prob. 4GP Ch. 2.7 - Prob. 5GP Ch. 2.7 - Prob. 6GP Ch. 2.7 - Prob. 7GP Ch. 2.7 - Prob. 8GP Ch. 2.7 - Prob. 9GP Ch. 2.7 - Prob. 10GP Ch. 2.7 - Prob. 11GP Ch. 2.7 - Prob. 12GP Ch. 2.7 - Prob. 1E Ch. 2.7 - Prob. 2E Ch. 2.7 - Prob. 3E Ch. 2.7 - Prob. 4E Ch. 2.7 - Prob. 5E Ch. 2.7 - Prob. 6E Ch. 2.7 - Prob. 7E Ch. 2.7 - Prob. 8E Ch. 2.7 - Prob. 9E Ch. 2.7 - Prob. 10E Ch. 2.7 - Prob. 11E Ch. 2.7 - Prob. 12E Ch. 2.7 - Prob. 13E Ch. 2.7 - Prob. 14E Ch. 2.7 - Prob. 15E Ch. 2.7 - Prob. 16E Ch. 2.7 - Prob. 17E Ch. 2.7 - Prob. 18E Ch. 2.7 - Prob. 19E Ch. 2.7 - Prob. 20E Ch. 2.7 - Prob. 21E Ch. 2.7 - Prob. 22E Ch. 2.7 - Prob. 23E Ch. 2.7 - Prob. 24E Ch. 2.7 - Prob. 25E Ch. 2.7 - Prob. 26E Ch. 2.7 - Prob. 27E Ch. 2.7 - Prob. 28E Ch. 2.7 - Prob. 29E Ch. 2.7 - Prob. 30E Ch. 2.7 - Prob. 31E Ch. 2.7 - Prob. 32E Ch. 2.7 - Prob. 33E Ch. 2.7 - Prob. 34E Ch. 2.7 - Prob. 35E Ch. 2.7 - Prob. 36E Ch. 2.7 - Prob. 37E Ch. 2.7 - Prob. 38E Ch. 2.7 - Prob. 39E Ch. 2.7 - Prob. 40E Ch. 2.7 - Prob. 41E Ch. 2.7 - Prob. 42E Ch. 2.7 - Prob. 43E Ch. 2.7 - Prob. 44E Ch. 2.7 - Prob. 45E Ch. 2.7 - Prob. 46E Ch. 2.7 - Prob. 47E Ch. 2.7 - Prob. 48E Ch. 2.7 - Prob. 49E Ch. 2.7 - Prob. 50E Ch. 2.7 - Prob. 51E Ch. 2.7 - Prob. 52E Ch. 2.7 - Prob. 53E Ch. 2.7 - Prob. 54E Ch. 2.7 - Prob. 55E Ch. 2.7 - Prob. 56E Ch. 2.7 - Prob. 57E Ch. 2.7 - Prob. 58E Ch. 2.7 - Prob. 59PS Ch. 2.7 - Prob. 60PS Ch. 2.7 - Prob. 61PS Ch. 2.7 - Prob. 62PS Ch. 2.7 - Prob. 63PS Ch. 2.7 - Prob. 64PS Ch. 2.7 - Prob. 65PS Ch. 2.8 - Prob. 1GP Ch. 2.8 - Prob. 2GP Ch. 2.8 - Prob. 3GP Ch. 2.8 - Prob. 4GP Ch. 2.8 - Prob. 5GP Ch. 2.8 - Prob. 1E Ch. 2.8 - Prob. 2E Ch. 2.8 - Prob. 3E Ch. 2.8 - Prob. 4E Ch. 2.8 - Prob. 5E Ch. 2.8 - Prob. 6E Ch. 2.8 - Prob. 7E Ch. 2.8 - Prob. 8E Ch. 2.8 - Prob. 9E Ch. 2.8 - Prob. 10E Ch. 2.8 - Prob. 11E Ch. 2.8 - Prob. 12E Ch. 2.8 - Prob. 13E Ch. 2.8 - Prob. 14E Ch. 2.8 - Prob. 15E Ch. 2.8 - Prob. 16E Ch. 2.8 - Prob. 17E Ch. 2.8 - Prob. 18E Ch. 2.8 - Prob. 19E Ch. 2.8 - Prob. 20E Ch. 2.8 - Prob. 21E Ch. 2.8 - Prob. 22E Ch. 2.8 - Prob. 23E Ch. 2.8 - Prob. 24E Ch. 2.8 - Prob. 25E Ch. 2.8 - Prob. 26E Ch. 2.8 - Prob. 27E Ch. 2.8 - Prob. 28E Ch. 2.8 - Prob. 29E Ch. 2.8 - Prob. 30E Ch. 2.8 - Prob. 31E Ch. 2.8 - Prob. 32E Ch. 2.8 - Prob. 33E Ch. 2.8 - Prob. 34E Ch. 2.8 - Prob. 35E Ch. 2.8 - Prob. 36E Ch. 2.8 - Prob. 37E Ch. 2.8 - Prob. 38E Ch. 2.8 - Prob. 39PS Ch. 2.8 - Prob. 40PS Ch. 2.8 - Prob. 41PS Ch. 2.8 - Prob. 42PS Ch. 2.8 - Prob. 43PS Ch. 2.8 - Prob. 44PS Ch. 2.8 - Prob. 1Q Ch. 2.8 - Prob. 2Q Ch. 2.8 - Prob. 3Q Ch. 2.8 - Prob. 4Q Ch. 2.8 - Prob. 5Q Ch. 2.8 - Prob. 6Q Ch. 2.8 - Prob. 7Q Ch. 2.8 - Prob. 8Q Ch. 2.8 - Prob. 9Q Ch. 2.8 - Prob. 10Q Ch. 2.8 - Prob. 1MRPS Ch. 2.8 - Prob. 2MRPS Ch. 2.8 - Prob. 3MRPS Ch. 2.8 - Prob. 4MRPS Ch. 2.8 - Prob. 5MRPS Ch. 2.8 - Prob. 6MRPS Ch. 2.8 - Prob. 7MRPS Ch. 2 - Prob. 1VE Ch. 2 - Prob. 2VE Ch. 2 - Prob. 3VE Ch. 2 - Prob. 4VE Ch. 2 - Prob. 5REAE Ch. 2 - Prob. 6REAE Ch. 2 - Prob. 7REAE Ch. 2 - Prob. 8REAE Ch. 2 - Prob. 9REAE Ch. 2 - Prob. 10REAE Ch. 2 - Prob. 11REAE Ch. 2 - Prob. 12REAE Ch. 2 - Prob. 13REAE Ch. 2 - Prob. 14REAE Ch. 2 - Prob. 15REAE Ch. 2 - Prob. 16REAE Ch. 2 - 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Prob. 1P Ch. 2 - Prob. 2P Ch. 2 - Prob. 1TP Ch. 2 - Prob. 2TP Ch. 2 - Prob. 3TP Ch. 2 - Prob. 4TP Ch. 2 - Prob. 5TP Ch. 2 - Prob. 6TP Ch. 2 - Prob. 7TP Ch. 2 - Prob. 8TP Ch. 2 - Prob. 9TP Ch. 2 - Prob. 10TP Ch. 2 - Prob. 11TP Ch. 2 - Prob. 12TP Ch. 2 - Prob. 13TP Ch. 2 - Prob. 14TP Ch. 2 - Prob. 15TP Ch. 2 - Prob. 16TP Ch. 2 - Prob. 17TP Ch. 2 - Prob. 18TP Ch. 2 - Prob. 19TP Ch. 2 - Prob. 20TP Ch. 2 - Prob. 21TP

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

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Chapter 2 Solutions