
Concept explainers
(a.)
To Complete: The given table.
It has been determined that the value of the second deposit for year 3 is
Given:
An amount of
The growth factor
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
The growth factor is
Then, the value of the second deposit for year 3 is
The value of the third deposit for year 3 is
The growth factor is
Then, the value of the third deposit for year 4 is
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
(b.)
To Write: A polynomial function that gives the value
It has been determined that a polynomial function that gives the value
Given:
An amount of
The growth factor
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
Then, the value
Conclusion:
It has been determined that a polynomial function that gives the value
(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
Given:
An amount of
The growth factor
The following table shows the value of the deposits over the four-year period:
The amount to be saved is
Concept used:
The required growth factor and thus the required annual interest rate can be obtained by plugging in the given value of
Calculation:
As determined previously, the value
It is given that the amount to be saved is
Then,
Put
Simplifying,
On further simplification,
Finally,
The graph of the above polynomial is given as,
From the above graph, the only real root of the polynomial equation is
Hence, this is the required growth factor.
Now, as assumed,
Put
Solving,
This implies that the required annual interest rate is approximately
Conclusion:
It has been determined that the required growth factor is approximately
Chapter 2 Solutions
Mcdougal Littell Algebra 2: Student Edition (c) 2004 2004
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