From 2005 to 2013, the median usual weekly earnings of full-time wage and salary workers were approximately E(x) 261x X + 8.84 + 647 dollars where x is the number of years after 2005. Differentiating using the Quotient Rule, find E'(4). (Round your answers to two decimal places.) $ Interpret your answer. Median weekly earnings are --Select--- by this amount per year in 2009. Differentiating using the Quotient Rule, find E'(8). (Round your answers to two decimal places.) $ Interpret your answer. Median weekly earnings are ✔ ---Select--- this amount per year in 2013.
From 2005 to 2013, the median usual weekly earnings of full-time wage and salary workers were approximately E(x) 261x X + 8.84 + 647 dollars where x is the number of years after 2005. Differentiating using the Quotient Rule, find E'(4). (Round your answers to two decimal places.) $ Interpret your answer. Median weekly earnings are --Select--- by this amount per year in 2009. Differentiating using the Quotient Rule, find E'(8). (Round your answers to two decimal places.) $ Interpret your answer. Median weekly earnings are ✔ ---Select--- this amount per year in 2013.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![### Analysis of Median Usual Weekly Earnings (2005-2013)
From 2005 to 2013, the median usual weekly earnings of full-time wage and salary workers were approximately modeled by the function:
\[ E(x) = \frac{261x}{x + 8.84} + 647 \]
where \( x \) is the number of years after 2005.
### Task 1: Compute the Rate of Change in 2009
1. **Differentiate using the Quotient Rule:**
Find \( E'(4) \). (Round your answers to two decimal places.)
Input: $______
2. **Interpret your answer:**
Median weekly earnings are
\[ \text{Select Option: ---Select--- \/ rising \/ falling } \]
by this amount per year in **2009**.
### Task 2: Compute the Rate of Change in 2013
1. **Differentiate using the Quotient Rule:**
Find \( E'(8) \). (Round your answers to two decimal places.)
Input: $______
2. **Interpret your answer:**
Median weekly earnings are
\[ \text{Select Option: ---Select--- \/ rising \/ falling } \]
by this amount per year in **2013**.
### Detailed Explanation of Graphs and Diagrams
**Graph Description:**
The image does not contain actual graphs but involves mathematical modeling. To understand how the earnings change, differentiation is applied to the given function \( E(x) \). The Quotient Rule is necessary to find the rate of change of earnings in specific years such as 2009 and 2013.
**Quotient Rule:**
The function \(E(x)\) contains a quotient and to differentiate it, the Quotient Rule is applied:
\[ ( \frac{u}{v} )' = \frac{u'v - uv'}{v^2} \]
Where:
- \( u = 261x \)
- \( v = x + 8.84 \)
### Need Help?
For any assistance, click on the "Read It" button.
---
The provided mathematical function helps to approximate and analyze the median weekly earnings over the given years. By differentiating, we can interpret whether the earnings are rising or falling at specific points in time.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7e0cd55c-6f84-412a-ac81-9a79eaea810f%2Fdbce89f1-ee55-433b-9867-2643fac6eab0%2Fig0bae_processed.png&w=3840&q=75)
Transcribed Image Text:### Analysis of Median Usual Weekly Earnings (2005-2013)
From 2005 to 2013, the median usual weekly earnings of full-time wage and salary workers were approximately modeled by the function:
\[ E(x) = \frac{261x}{x + 8.84} + 647 \]
where \( x \) is the number of years after 2005.
### Task 1: Compute the Rate of Change in 2009
1. **Differentiate using the Quotient Rule:**
Find \( E'(4) \). (Round your answers to two decimal places.)
Input: $______
2. **Interpret your answer:**
Median weekly earnings are
\[ \text{Select Option: ---Select--- \/ rising \/ falling } \]
by this amount per year in **2009**.
### Task 2: Compute the Rate of Change in 2013
1. **Differentiate using the Quotient Rule:**
Find \( E'(8) \). (Round your answers to two decimal places.)
Input: $______
2. **Interpret your answer:**
Median weekly earnings are
\[ \text{Select Option: ---Select--- \/ rising \/ falling } \]
by this amount per year in **2013**.
### Detailed Explanation of Graphs and Diagrams
**Graph Description:**
The image does not contain actual graphs but involves mathematical modeling. To understand how the earnings change, differentiation is applied to the given function \( E(x) \). The Quotient Rule is necessary to find the rate of change of earnings in specific years such as 2009 and 2013.
**Quotient Rule:**
The function \(E(x)\) contains a quotient and to differentiate it, the Quotient Rule is applied:
\[ ( \frac{u}{v} )' = \frac{u'v - uv'}{v^2} \]
Where:
- \( u = 261x \)
- \( v = x + 8.84 \)
### Need Help?
For any assistance, click on the "Read It" button.
---
The provided mathematical function helps to approximate and analyze the median weekly earnings over the given years. By differentiating, we can interpret whether the earnings are rising or falling at specific points in time.
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