59. In an exponential decay function, the base of the exponent is a value between 0 and 1. Thus, for some number b> 1, the exponential decay function can be written as f(r) = a· (-)". Use this formula, along %3D with the fact that b = e", to show that an exponential decay function takes the form f(r) = a(e) for %3D some positive number n. II
59. In an exponential decay function, the base of the exponent is a value between 0 and 1. Thus, for some number b> 1, the exponential decay function can be written as f(r) = a· (-)". Use this formula, along %3D with the fact that b = e", to show that an exponential decay function takes the form f(r) = a(e) for %3D some positive number n. II
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![### Understanding Exponential Decay Functions
In an exponential decay function, the base of the exponent is a value between 0 and 1. Thus, for some number \( b > 1 \), the exponential decay function can be written as:
\[ f(x) = a \cdot \left( \frac{1}{b} \right)^x. \]
Use this formula, along with the fact that \( b = e^n \), to show that an exponential decay function takes the form:
\[ f(x) = a(e)^{-nx} \]
for some positive number \( n \).
This transformation involves recognizing that the decay rate can be expressed using the natural exponential base \( e \), facilitating deeper analysis and understanding within mathematical contexts.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8e8b7e03-8b3f-4682-a21a-4c3c3b06b195%2F7c9292a4-4b62-421a-9eff-b708cc88885f%2Fv8p8wug_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Exponential Decay Functions
In an exponential decay function, the base of the exponent is a value between 0 and 1. Thus, for some number \( b > 1 \), the exponential decay function can be written as:
\[ f(x) = a \cdot \left( \frac{1}{b} \right)^x. \]
Use this formula, along with the fact that \( b = e^n \), to show that an exponential decay function takes the form:
\[ f(x) = a(e)^{-nx} \]
for some positive number \( n \).
This transformation involves recognizing that the decay rate can be expressed using the natural exponential base \( e \), facilitating deeper analysis and understanding within mathematical contexts.
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