(a)
To prove : The statement is
(a)
Explanation of Solution
Given information:
The statement is
Calculation:
And the table is:
1 | 2 |
10 | 2.5937 |
100 | 2.7048 |
1000 | 2.7169 |
10000 | 2.7181 |
100000 | 2.7183 |
The graph is shown below:
Therefore, the required given statement
(b)
To prove: The given statement.
(b)
Explanation of Solution
Given information:
The statement is
Calculation:
If
Then ,
Input,
10 | 6.1917 |
100 | 7.2446 |
1,000 | 7.3743 |
10,000 | 7.3876 |
100,000 | 7.389 |
7.3891 | |
7.3891 |
The graph is shown below:
If
Then ,
Input
10 | 13.786 |
100 | 19.219 |
1,000 | 19.996 |
10,000 | 20.077 |
100,000 | 20.085 |
20.086 | |
20.086 |
The graph is shown below:
Therefore, , the required given statement
(c)
To explain: The given statement.
(c)
Answer to Problem 56E
which is the formula for interest compounded continuously.
Explanation of Solution
Given information:
The idea of interest compounded continuously results from the compounding of interest over ever-shorter time periods.
Calculation:
The compound interest value is
Compounding interest over smaller and smaller periods means nn gets larger and larger. From part
So,
which is the formula for interest compounded continuously.
Chapter 6 Solutions
AP CALCULUS TEST PREP-WORKBOOK
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