Concept explainers
(a)
To find : the time necessary for P dollars to double.
(a)
![Check Mark](/static/check-mark.png)
Answer to Problem 72E
The time necessary for P dollars to double is
Explanation of Solution
Given information : Amount invested
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, number of times interest applied per time period n and annual interest rate r (in decimal form) is given by the formula:
Logarithmic property:
Calculation:
Description | Steps |
Substitute the given information in the formula | |
Use symmetric property of equality which states that if | |
Dividing 2500 on both sides of the equation | |
Simplify fraction in both sides of the equation |
Calculation (Continued):
Description | Steps |
Take natural logarithm on both sides of the equation | |
Apply the logarithmic rule | |
Divide by 0.0375 on both sides | |
Simplify fraction on both sides of the equation |
Conclusion:
It would take time of 18.48years for $2500 dollars to double when it is invested at interest rate
(b)
To find : the time necessary for P dollars to triple.
(b)
![Check Mark](/static/check-mark.png)
Answer to Problem 72E
The time necessary for P dollars to triple is
Explanation of Solution
Given information : Amount invested
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, number of times interest applied per time period n and annual interest rate r (in decimal form) is given by the formula:
Logarithmic property:
Calculation:
Description | Steps |
Substitute the given information in the formula | |
Use symmetric property of equality which states that if | |
Dividing 2500 on both sides of the equation | |
Simplify fraction in both sides of the equation |
Calculation (Continued):
Description | Steps |
Take natural logarithm on both sides of the equation | |
Apply the logarithmic rule | |
Divide by 0.0375 on both sides | |
Simplify fraction on both sides of the equation |
Conclusion:
It would take time of 29.3 years for $2500 dollars to triple when it is invested at interest rate
Chapter 3 Solutions
EBK PRECALCULUS W/LIMITS
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