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...
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Question
(4) Please show how you solved the equation.
![**Problem:**
Solve \( e^{3t} = 2000 \) for \( t \).
---
**Solution:**
To find \( t \), we take the natural logarithm on both sides of the equation:
\[
\ln(e^{3t}) = \ln(2000)
\]
This simplifies using the property of logarithms:
\[
3t = \ln(2000)
\]
Next, we solve for \( t \):
\[
t = \frac{\ln(2000)}{3}
\]
Finally, calculate the value of \( t \) and round to three decimal places.
**Answer:**
\[ t \approx \boxed{\phantom{0}} \] (Round to three decimal places as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9dc72e72-cadd-4409-82bd-d52418d83748%2Fac7cc38f-8097-4f96-bb83-b4ed99a86d3b%2Fedjx7mg_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem:**
Solve \( e^{3t} = 2000 \) for \( t \).
---
**Solution:**
To find \( t \), we take the natural logarithm on both sides of the equation:
\[
\ln(e^{3t}) = \ln(2000)
\]
This simplifies using the property of logarithms:
\[
3t = \ln(2000)
\]
Next, we solve for \( t \):
\[
t = \frac{\ln(2000)}{3}
\]
Finally, calculate the value of \( t \) and round to three decimal places.
**Answer:**
\[ t \approx \boxed{\phantom{0}} \] (Round to three decimal places as needed.)
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