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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![To solve the equation \( e^{3t} = 1800 \) for \( t \):
1. Take the natural logarithm (ln) on both sides of the equation:
\[
\ln(e^{3t}) = \ln(1800)
\]
2. Simplify the left side using the property \(\ln(e^x) = x\):
\[
3t = \ln(1800)
\]
3. Solve for \( t \):
\[
t = \frac{\ln(1800)}{3}
\]
4. Calculate the value and round to three decimal places as needed.
Final answer:
\[ t \approx \boxed{} \] (Fill in the blank with the calculated value).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe2539764-cbb6-4f84-96a1-bc799fc276f3%2F3bd69ea1-ab6d-443b-8835-d84ab3c7d5c0%2F19xjfd_processed.png&w=3840&q=75)
Transcribed Image Text:To solve the equation \( e^{3t} = 1800 \) for \( t \):
1. Take the natural logarithm (ln) on both sides of the equation:
\[
\ln(e^{3t}) = \ln(1800)
\]
2. Simplify the left side using the property \(\ln(e^x) = x\):
\[
3t = \ln(1800)
\]
3. Solve for \( t \):
\[
t = \frac{\ln(1800)}{3}
\]
4. Calculate the value and round to three decimal places as needed.
Final answer:
\[ t \approx \boxed{} \] (Fill in the blank with the calculated value).
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