Precalculus with Limits
3rd Edition
ISBN: 9781133947202
Author: Ron Larson
Publisher: Cengage Learning
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Question
Chapter 3.5, Problem 12E
To determine
To find : the Initial investment and Annual % Rate.
Expert Solution & Answer
Answer to Problem 12E
The initial investment is
The Annual % Rate is
Explanation of Solution
Given information : Time to double is 12 years&Amount after 10 years is $2000.00
Concept Involved:
Solving for a variable means getting the variable alone in one side of the equation by undoing whatever operation is done to it.
Formula Used:
For continuous compounding, after t years, the balance A in an account with principal P and annual interest rate r (in decimal form) is given by the formula:
Logarithmic property:
Calculation:
| Description | Steps |
| We are given time to double is 12 years, so let us substitute A=2P in equation | |
| Use symmetric property of equality which states that if a = b then b = a to rewrite the equation | |
| In the process of solving for r divide by P on both sides | |
| Simplify fraction on both sides of the equation | |
| Take natural logarithm on both sides | |
| Apply the logarithmic rule | |
| Divide by 12 on both sides |
Calculation (Continued):
| Description | Steps |
| Simplify fraction on both sides of the equation | |
| Rewrite the decimal as percentage | |
| Substitute the given information in the formula | |
| Use symmetric property of equality which states that if a = b then b = a to rewrite the equation | |
| Divide by | |
| Simplify fraction on both sides of the equation |
Conclusion:
| Initial Investment | Annual % Rate | Time to Double | Amount After 10 years |
| $1122 | 12 years (Given) | $10000(Given) |
Chapter 3 Solutions
Precalculus with Limits
Ch. 3.1 - Prob. 1ECh. 3.1 - Prob. 2ECh. 3.1 - Prob. 3ECh. 3.1 - Prob. 4ECh. 3.1 - Prob. 5ECh. 3.1 - Prob. 6ECh. 3.1 - Prob. 7ECh. 3.1 - Prob. 8ECh. 3.1 - Prob. 9ECh. 3.1 - Prob. 10E
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Calculus
ISBN:9781337552516
Author:Ron Larson, Bruce H. Edwards
Publisher:Cengage Learning
01 - What Is A Differential Equation in Calculus? Learn to Solve Ordinary Differential Equations.; Author: Math and Science;https://www.youtube.com/watch?v=K80YEHQpx9g;License: Standard YouTube License, CC-BY
Higher Order Differential Equation with constant coefficient (GATE) (Part 1) l GATE 2018; Author: GATE Lectures by Dishank;https://www.youtube.com/watch?v=ODxP7BbqAjA;License: Standard YouTube License, CC-BY
Solution of Differential Equations and Initial Value Problems; Author: Jefril Amboy;https://www.youtube.com/watch?v=Q68sk7XS-dc;License: Standard YouTube License, CC-BY