Concept explainers
To check: The given statement: “The compound interest formula is an exponential growth function” is true or false.
Answer to Problem 1MP
True.
Explanation of Solution
Given Information: The compound interest formula is
Formula used:
An exponential growth can be modeled by the function
The base b is called growth factor.
The compound interest formula,
∴ The given statement: The compound interest formula is an exponential growth function is true.
(b)
To check the given statement: “The compound interest formula is an exponential decay function” is true or false
(b)
Answer to Problem 1MP
False.
Explanation of Solution
Given Information: The compound interest formula is
Formula used:
An exponential decay can be modeled by the function
The base b is called decay factor.
The compound interest formula,
∴ The given statement: The compound interest formula is an exponential decay function is false
(c)
To check the given statement: “For the CD from Bank West,
(c)
Answer to Problem 1MP
False.
Explanation of Solution
Given Information: Details of the West Bank is shown below:
Bank | CD Length | AnnualInterest Rate | Frequency of compounding |
Bank West | 6 years | 3.8 | Quarterly |
In the formula for compound interest,
For Bank West, it is given that the interest is compounded quarterly.
∴ The number of times interest applied per time period is 4
That is,
∴The given statement: For the CD from Bank West,
(d)
To check the given statement: “For the CD from First Bank,
(d)
Answer to Problem 1MP
True.
Explanation of Solution
Given Information: Details of the First Bank is shown below:
Bank | CD Length | AnnualInterest Rate | Frequency of compounding |
First Bank | 5 years | 4.3 | Monthly |
In the formula for compound interest,
For the First Bank it is given that the interest is compounded monthly and time period of the CD is 5 years.
That is,
∴
∴ The given statement: For the CD from Bank First
(e)
To check the given statement: “The growth /decay factor for the CD from Bank West is
(e)
Answer to Problem 1MP
True.
Explanation of Solution
Given Information: Details of the West Bank is shown below:
Bank | CD Length | AnnualInterest Rate | Frequency of compounding |
Bank West | 6 years | 3.8 | Quarterly |
The compound interest formula,
n represents number of times interest applied per time period and t represents the time period.
For Bank West, it is given that the interest is compounded quarterly and time period is 6 years.
∴ The growth factor
=
∴ The given statement: The growth /decay factor for the CD from Bank West is
(f)
To check the given statement: “The growth /decay factor for the CD from Bank West is
(f)
Answer to Problem 1MP
False.
Explanation of Solution
From part (e) it has been find that the growth factor
for the CD from Bank West is
∴ The given statement the growth /decay factor for the CD from Bank West is
(g)
To check the given statement: “The growth /decay factor for the CD from Bank First is
(g)
Answer to Problem 1MP
Explanation of Solution
Given Information: Details of the First Bank is shown below:
Bank | CD Length | AnnualInterest Rate | Frequency of compounding |
First Bank | 5 years | 4.3 | Monthly |
For the First bank:
Growth Factor for the CD from First Bank =
=
=
Clearly the Growth Factor for the CD from First Bank is not equal to
∴The given statement: “The growth /decay factor for the CD from Bank First is
Chapter 7 Solutions
High School Math 2015 Common Core Algebra 1 Student Edition Grade 8/9
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