Concept explainers
To explain if the times required for the investments in the given problem for the amount to quadruple is twice as long as the times for them to double.
Explanation of Solution
Given Information:
The given values are-
Calculation:
The answer is Yes, which is explained through the following example.
Let us use the formula for continuous compounding, the balance in the account is
For the given principal and rate, the amount is
Now, the time required for the balance to double is calculated as:
Let
Now,
Dividing both sides by 2500
Taking natural logarithm on both sides
Using the inverse property,
Dividing both sides by 0.05
Now, the time required for the balance to quadruple is calculated as:
Let
Now,
Dividing both sides by 2500
Taking natural logarithm on both sides
Dividing both sides by 0.05
Hence, the time required for the amount to quadruple is twice the time for the amount to double.
Chapter 3 Solutions
EBK PRECALCULUS W/LIMITS
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning