In 1991, the cost of mailing a 1 oz. first-class letter was 29 cents, and the inflation rate was 4.6%. If the inflation rate stayed constant, the function C(t) = 0.29(1.046) would represent the cost of mailing a first-class letter as a function of years since 1991. 1. If the function given holds true, in what year would the cost of mailing a first-class letter reach 60 cents?
In 1991, the cost of mailing a 1 oz. first-class letter was 29 cents, and the inflation rate was 4.6%. If the inflation rate stayed constant, the function C(t) = 0.29(1.046) would represent the cost of mailing a first-class letter as a function of years since 1991. 1. If the function given holds true, in what year would the cost of mailing a first-class letter reach 60 cents?
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
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![### Cost of Mailing a First-Class Letter Over Time
In 1991, the cost of mailing a 1 oz. first-class letter was 29 cents, and the inflation rate was 4.6%. If the inflation rate stayed constant, the function \( C(t) = 0.29(1.046)^t \) would represent the cost of mailing a first-class letter as a function of years since 1991.
1. **Question**: If the function given holds true, in what year would the cost of mailing a first-class letter reach 60 cents?
To find the year in which the cost reaches 60 cents, we need to solve for \( t \) in the equation:
\[ 0.29(1.046)^t = 0.60 \]
This simplifies to:
\[ (1.046)^t = \frac{0.60}{0.29} \]
\[ t = \log_{1.046} \left( \frac{0.60}{0.29} \right) \]
Using a calculator to find the value:
\[ t = \log_{1.046} (2.069) \approx 16.47 \]
So, approximately 16.47 years after 1991, the cost would reach 60 cents.
Since the question asks for the year:
\[ 1991 + 16.47 \approx 2007.47 \]
Therefore, according to the given function, the cost of mailing a first-class letter would reach 60 cents around the year 2008.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F414899e3-a595-438f-9c86-72ba03c624e1%2F018aa3c1-32f2-4ec4-829e-f7d24b0de755%2F4tw3ctc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Cost of Mailing a First-Class Letter Over Time
In 1991, the cost of mailing a 1 oz. first-class letter was 29 cents, and the inflation rate was 4.6%. If the inflation rate stayed constant, the function \( C(t) = 0.29(1.046)^t \) would represent the cost of mailing a first-class letter as a function of years since 1991.
1. **Question**: If the function given holds true, in what year would the cost of mailing a first-class letter reach 60 cents?
To find the year in which the cost reaches 60 cents, we need to solve for \( t \) in the equation:
\[ 0.29(1.046)^t = 0.60 \]
This simplifies to:
\[ (1.046)^t = \frac{0.60}{0.29} \]
\[ t = \log_{1.046} \left( \frac{0.60}{0.29} \right) \]
Using a calculator to find the value:
\[ t = \log_{1.046} (2.069) \approx 16.47 \]
So, approximately 16.47 years after 1991, the cost would reach 60 cents.
Since the question asks for the year:
\[ 1991 + 16.47 \approx 2007.47 \]
Therefore, according to the given function, the cost of mailing a first-class letter would reach 60 cents around the year 2008.
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