Algebra 2: New York Edition (holt Mcdougal Larson Algebra 2)
2nd Edition
ISBN: 9780618912407
Author: MCDOUGAL LITTEL
Publisher: Mcdougal Littel
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Expert Solution & Answer
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
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
Algebra 2: New York Edition (holt Mcdougal Larson Algebra 2)
Ch. 2.1 - Prob. 1GPCh. 2.1 - Prob. 2GPCh. 2.1 - Prob. 3GPCh. 2.1 - Prob. 4GPCh. 2.1 - Prob. 5GPCh. 2.1 - Prob. 6GPCh. 2.1 - Prob. 7GPCh. 2.1 - Prob. 8GPCh. 2.1 - Prob. 1ECh. 2.1 - Prob. 2E
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- 10) Multiply (8m + 3)² A) 8m²+11m+6 B) m² + 48m+9 C) 64m²+48m+9 D) 16m²+11m+6arrow_forwardLet R be field and X= R³/s Vector space over R M=(a,b,c)labic, e Rra+b= 3- <3 Show that Ms and why with proof. 1) is convexset and affine set of botost ii) is blanced set and symmetirs set of x iii) is hy per space and hyper plane ofx or hot iii) find f:MR st kerf = M 18/103 and finnd fiM→R/{0} st M= {xEX, f(t) = x, texiαER? jiii) show that Mis Maxsubspace or not and Mis a max. affine set or not.arrow_forwardFind The partial fraction decomposition for each The following 2× B) (x+3) a 3 6 X-3x+2x-6arrow_forward
- 1) Find the partial feraction decomposition for each of 5- X 2 2x+x-1 The following: 3 B) 3 X + 3xarrow_forwardT={(−7,1),(1,−1),(6,−8),(2,8)} Find the domain and range of the inverse. Express your answer as a set of numbers.arrow_forwardT={(−7,1),(1,−1),(6,−8),(2,8)}. Find the inverse. Express your answer as a set of ordered pairs.arrow_forward
- 2.8.1arrow_forwardKate, Luke, Mary and Nancy are sharing a cake. The cake had previously been divided into four slices (s1, s2, s3 and s4). The following table shows the values of the slices in the eyes of each player. What is fair share to nancy? S1 S2 S3 S4 Kate $4.00 $6.00 $6.00 $4.00 Luke $5.30 $5.00 $5.25 $5.45 Mary $4.25 $4.50 $3.50 $3.75 Nancy $6.00 $4.00 $4.00 $6.00arrow_forwardKate, Luke, Mary and Nancy are sharing a cake. The cake had previously been divided into four slices (s1, s2, s3 and s4). The following table shows the values of the slices in the eyes of each player. S1 S2 S3 S4 Kate $4.00 $6.00 $6.00 $4.00 Luke $5.30 $5.00 $5.25 $5.45 Mary $4.25 $4.50 $3.50 $3.75 Nancy $6.00 $4.00 $4.00 $6.00 how much is the cak worth to maryarrow_forward
- Kate, Luke, Mary and Nancy are sharing a cake. The cake had previously been divided into four slices (s1, s2, s3 and s4). The following table shows the values of the slices in the eyes of each player. What is the threshold of fair share for Luke? S1 S2 S3 S4 Kate $4.00 $6.00 $6.00 $4.00 Luke $5.30 $5.00 $5.25 $5.45 Mary $4.25 $4.50 $3.50 $3.75 Nancy $6.00 $4.00 $4.00 $6.00arrow_forward2. A microwave manufacturing firm has determined that their profit function is P(x)=-0.0014x+0.3x²+6x-355 , where is the number of microwaves sold annually. a. Graph the profit function using a calculator. b. Determine a reasonable viewing window for the function. c. Approximate all of the zeros of the function using the CALC menu of your calculator. d. What must be the range of microwaves sold in order for the firm to profit?arrow_forwardA clothing manufacturer's profitability can be modeled by p (x)=-x4 + 40x² - 144, where .x is the number of items sold in thousands and p (x) is the company's profit in thousands of dollars. a. Sketch the function on your calculator and describe the end behavior. b. Determine the zeros of the function. c. Between what two values should the company sell in order to be profitable? d. Explain why only two of the zeros are considered in part c.arrow_forward
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