Textbook Question
Use the formula for continuous compounding to solve Exercises 84–85. What annual rate, to the nearest percent, is required for an investment subject to continuous compounding to triple in 5 years?
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6. Exponential & Logarithmic Functions
Solving Exponential and Logarithmic Equations
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Join thousands of students who trust us to help them ace their exams!Watch the first videoMultiple Choice
Solve the exponential equation.
A
2
B
5
C
9
D
– 5
Verified step by step guidance1
First, recognize that the equation is in the form of an exponential equation: \( 4^{x+7} = 16 \).
Notice that 16 can be rewritten as a power of 4, since \( 16 = 4^2 \).
Substitute \( 16 \) with \( 4^2 \) in the equation, resulting in \( 4^{x+7} = 4^2 \).
Since the bases are the same, you can set the exponents equal to each other: \( x + 7 = 2 \).
Solve for \( x \) by subtracting 7 from both sides of the equation: \( x = 2 - 7 \).
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