Terius writes the function P (t) = 56, 280e0.022t, where t is time in years, to represent the future population of his city based on projected population growth ra He claims that it will take less than 10 years for the population of his city to become 85, 000 and shows the following work to support his claim. 85,000 = 56, 280e0.022t 1.5103 = 0.022t log 1.5103 = 0.022t log e log 1.5103 = 0.022t 8.1 t Which TWO statements are TRUE? A B C D E Terius did not correctly rewrite log e0.022t Terius did not correctly determine the value of log e. Terius's claim is correct even though there is a mistake in his work. Terius's claim is correct because there are no actual mistakes in his work. Terius could have applied the In function
Terius writes the function P (t) = 56, 280e0.022t, where t is time in years, to represent the future population of his city based on projected population growth ra He claims that it will take less than 10 years for the population of his city to become 85, 000 and shows the following work to support his claim. 85,000 = 56, 280e0.022t 1.5103 = 0.022t log 1.5103 = 0.022t log e log 1.5103 = 0.022t 8.1 t Which TWO statements are TRUE? A B C D E Terius did not correctly rewrite log e0.022t Terius did not correctly determine the value of log e. Terius's claim is correct even though there is a mistake in his work. Terius's claim is correct because there are no actual mistakes in his work. Terius could have applied the In function
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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![Terius writes the function \( P(t) = 56,280e^{0.022t} \), where \( t \) is time in years, to represent the future population of his city based on projected population growth rates.
He claims that it will take less than 10 years for the population of his city to become 85,000 and shows the following work to support his claim.
\[
85,000 = 56,280e^{0.022t}
\]
\[
1.5103 = e^{0.022t}
\]
\[
\log 1.5103 = 0.022t \log e
\]
\[
\log 1.5103 = 0.022t
\]
\[
8.1 \approx t
\]
### Which TWO statements are TRUE?
- [ ] A. Terius did not correctly rewrite \(\log e^{0.022t}\).
- [ ] B. Terius did not correctly determine the value of \(\log e\).
- [ ] C. Terius's claim is correct even though there is a mistake in his work.
- [ ] D. Terius's claim is correct because there are no actual mistakes in his work.
- [ ] E. Terius could have applied the ln function instead of the \(\log\).
The analysis involves solving an exponential equation to find \( t \), the time in years. Terius uses logarithms to solve for \( t \), ultimately finding it to be approximately 8.1 years, which supports his claim of less than 10 years. The problem presents a multiple-choice question assessing understanding of logarithmic properties and their application.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F17a2d8ab-b196-429b-9620-8f2501e2e071%2F92babeda-8d93-4cd5-9e4b-c888308dfcfe%2F6xhs5r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Terius writes the function \( P(t) = 56,280e^{0.022t} \), where \( t \) is time in years, to represent the future population of his city based on projected population growth rates.
He claims that it will take less than 10 years for the population of his city to become 85,000 and shows the following work to support his claim.
\[
85,000 = 56,280e^{0.022t}
\]
\[
1.5103 = e^{0.022t}
\]
\[
\log 1.5103 = 0.022t \log e
\]
\[
\log 1.5103 = 0.022t
\]
\[
8.1 \approx t
\]
### Which TWO statements are TRUE?
- [ ] A. Terius did not correctly rewrite \(\log e^{0.022t}\).
- [ ] B. Terius did not correctly determine the value of \(\log e\).
- [ ] C. Terius's claim is correct even though there is a mistake in his work.
- [ ] D. Terius's claim is correct because there are no actual mistakes in his work.
- [ ] E. Terius could have applied the ln function instead of the \(\log\).
The analysis involves solving an exponential equation to find \( t \), the time in years. Terius uses logarithms to solve for \( t \), ultimately finding it to be approximately 8.1 years, which supports his claim of less than 10 years. The problem presents a multiple-choice question assessing understanding of logarithmic properties and their application.
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