EBK PRECALCULUS W/LIMITS
4th Edition
ISBN: 9781337516853
Author: Larson
Publisher: CENGAGE CO
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Question
Chapter 3.4, Problem 45E
To determine
To find : solution to the exponential equation algebraically.
Expert Solution & Answer
Answer to Problem 45E
The solution to the equation (1+0.065365)365t=4 is t≈21.330 _
Explanation of Solution
Given information: (1+0.065365)365t=4
Concept Involved:
The word “solve” means the process of finding the value of t that makes the equation true. In order to solve we need to undo whatever is done to t .
Formula Used
- lnmn=n(lnm)
Calculation:
Take natural logarithm on both sides of the equation
ln(1+0.065365)365t=ln4
Use the logarithmic property lnmn=n(lnm) on both sides of the equation to rewrite it
365t⋅ln(1+0.065365)=ln4
Divide 365ln(1+0.065365) on both sides of the equation
365t⋅ln(1+0.065365)÷(365ln(1+0.065365))=ln4÷(365ln(1+0.065365))
Simplify fraction in both sides of the equation
t≈21.3295045
Check for extraneous solution by substituting the result in the original equation.
t≈21.3295045 makes the original equation TRUE
Conclusion:
The solution to the equation (1+0.065365)365t=4 is t≈21.330 _
Chapter 3 Solutions
EBK PRECALCULUS W/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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