Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Related questions
Question
100%
![**Problem Statement:**
Find the inverse function for
\[ f(t) = 41e^{0.25t} \]
**Solution:**
\[ f^{-1}(t) = \]
**Instructions:**
To find the inverse function \( f^{-1}(t) \), follow these steps:
1. Start with the equation \( y = 41e^{0.25t} \).
2. Swap \( y \) and \( t \) to find the inverse: \( t = 41e^{0.25y} \).
3. Solve for \( y \):
- Divide both sides by 41: \( \frac{t}{41} = e^{0.25y} \).
- Take the natural logarithm of both sides:
\[ \ln\left(\frac{t}{41}\right) = 0.25y \]
- Solve for \( y \) by dividing by 0.25:
\[ y = \frac{\ln\left(\frac{t}{41}\right)}{0.25} \]
This yields the inverse function:
\[ f^{-1}(t) = \frac{\ln\left(\frac{t}{41}\right)}{0.25} \]
Place your solution in the box provided in the original problem.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0d404c5d-4d55-46c0-aff4-29578c5eba85%2F5a7151ad-1b32-4707-ba8d-023c8fb8048f%2Fpmwpxva_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the inverse function for
\[ f(t) = 41e^{0.25t} \]
**Solution:**
\[ f^{-1}(t) = \]
**Instructions:**
To find the inverse function \( f^{-1}(t) \), follow these steps:
1. Start with the equation \( y = 41e^{0.25t} \).
2. Swap \( y \) and \( t \) to find the inverse: \( t = 41e^{0.25y} \).
3. Solve for \( y \):
- Divide both sides by 41: \( \frac{t}{41} = e^{0.25y} \).
- Take the natural logarithm of both sides:
\[ \ln\left(\frac{t}{41}\right) = 0.25y \]
- Solve for \( y \) by dividing by 0.25:
\[ y = \frac{\ln\left(\frac{t}{41}\right)}{0.25} \]
This yields the inverse function:
\[ f^{-1}(t) = \frac{\ln\left(\frac{t}{41}\right)}{0.25} \]
Place your solution in the box provided in the original problem.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 11 images
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning