Concept explainers
a.
To use tables to give a numerical argument that
a.
Answer to Problem 57E
x | y |
1 | 2 |
10 | 2.5937 |
100 | 2.7048 |
1000 | 2.7169 |
10000 | 2.7181 |
100000 | 2.7183 |
Graph is,
Explanation of Solution
Given Information: The function is,
Calculation:
As per the given problem,
x | y |
1 | 2 |
10 | 2.5937 |
100 | 2.7048 |
1000 | 2.7169 |
10000 | 2.7181 |
100000 | 2.7183 |
Graph is,
b.
For several different values of r, give numerical and graphical evidence that
b.
Answer to Problem 57E
The annuity will run out of fund at
Explanation of Solution
Given Information: The function is,
Calculation:
As per the given problem
If
10 | 6.1917 |
100 | 7.2446 |
1000 | 7.3743 |
10000 | 7.3876 |
100000 | 7.389 |
1000000 | 7.3891 |
10000000 | 7.3891 |
To verify the limit graphically, input
If
10 | 13.786 |
100 | 19.219 |
1000 | 19.996 |
10000 | 20.077 |
100000 | 20.085 |
1000000 | 20.086 |
10000000 | 20.086 |
To verify the limit graphically, input
If
10 | 1.6289 |
100 | 1.6467 |
1000 | 1.6485 |
10000 | 1.6487 |
100000 | 1.6487 |
To verify the limit graphically, input
c.
Explain why compounding interest over smaller and smaller periods of time leads to the concept of interest compounded continuously.
c.
Answer to Problem 57E
See calculation part.
Explanation of Solution
Given Information: Compounding interest over smaller and smaller periods of time leads to the concept of interest compounded continuously.
Calculation:
As per the given problem,
The compound interest formula is
Chapter 7 Solutions
Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
Additional Math Textbook Solutions
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