110x-11,000 The function f(x) a40, 30 sxs 100, models the tax revenue, f(x), in tens of billions of dollars, in terms of the tax rate, x. The graph of this function is shown to the right. It illustrates tax revenue decreasing dramatically as the tax rate increases. At a tax rate of 100%, the government takes all our money and no one has an incentive to work. With no income earned, zero dollars in tax revenue is generated. Complete parts (a) through (c) below. Tar Rate a. Find f(30). 1(30)- (Round to the nearest integer as needed.) Interpret your result. Choose the correct answer below. O A. When the tax rate is 85%, $300 billion in tax revenue is generated. OB. Ir the tax rate increases 85%, an additional $300 billion in revenue is generated. Oc. When the tax rate is 30%, $700 billion in tax revenue is generated. OD. if the tax rate increases 30%, an additional $700 billion in revenue is generated. Identify the solution as a point on the graph. Choose the correct graph below. OD. O B OA
110x-11,000 The function f(x) a40, 30 sxs 100, models the tax revenue, f(x), in tens of billions of dollars, in terms of the tax rate, x. The graph of this function is shown to the right. It illustrates tax revenue decreasing dramatically as the tax rate increases. At a tax rate of 100%, the government takes all our money and no one has an incentive to work. With no income earned, zero dollars in tax revenue is generated. Complete parts (a) through (c) below. Tar Rate a. Find f(30). 1(30)- (Round to the nearest integer as needed.) Interpret your result. Choose the correct answer below. O A. When the tax rate is 85%, $300 billion in tax revenue is generated. OB. Ir the tax rate increases 85%, an additional $300 billion in revenue is generated. Oc. When the tax rate is 30%, $700 billion in tax revenue is generated. OD. if the tax rate increases 30%, an additional $700 billion in revenue is generated. Identify the solution as a point on the graph. Choose the correct graph below. OD. O B OA
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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![**Transcription for Educational Website**
The given function is:
\[ f(x) = \frac{110x - 11,000}{x - 140} \]
This function models the tax revenue, \( f(x) \), in tens of billions of dollars, in relation to the tax rate, \( x \). The graph associated with this function depicts how tax revenue decreases as the tax rate increases. At a tax rate of 100%, the government collects no revenue due to the absence of incentive for work, leading to zero income earned and zero tax revenue.
**Tasks:**
**a. Find \( f(30) \).**
\( f(30) = \) [Input field]
(Round to the nearest integer as needed.)
**Interpret your result. Choose the correct answer below.**
- A. When the tax rate is 65%, $300 billion in tax revenue is generated.
- B. If the tax rate increases to 85%, an additional $300 billion in revenue is generated.
- C. When the tax rate is 30%, $700 billion in tax revenue is generated.
- D. If the tax rate increases 30%, an additional $700 billion in revenue is generated.
**Identify the solution as a point on the graph. Choose the correct graph below.**
- Option A: (Graph depicting a certain point)
- Option B: (Graph depicting a certain point)
- Option C: (Graph depicting a certain point)
- Option D: (Graph depicting a certain point)
**b. Rewrite the function using long division to perform:**
\[ \frac{110x - 11,000}{x - 140} \]
(Simplify your answer. If there is a remainder, type your answer as \( \text{quotient} + \frac{\text{remainder}}{\text{divisor}} \).)
Then use this new form of the function to find \( f(30) \).
\( f(30) = \) [Input field]
(Round to the nearest integer as needed.)
**c. Is \( f(x) \) a polynomial function? Explain your answer. Choose the correct answer below.**
- Yes, it is a polynomial function because the numerator is not fully factored.
- No, it is not a polynomial function because it cannot be written in the form \( a_nx^n + a_{n-1}x^{n-1} + \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa960f0fb-409e-4fad-9a6e-22a1d290aaa3%2F58a093b5-c563-4f41-841c-1cdb4c51d70e%2F7s1lp3_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Transcription for Educational Website**
The given function is:
\[ f(x) = \frac{110x - 11,000}{x - 140} \]
This function models the tax revenue, \( f(x) \), in tens of billions of dollars, in relation to the tax rate, \( x \). The graph associated with this function depicts how tax revenue decreases as the tax rate increases. At a tax rate of 100%, the government collects no revenue due to the absence of incentive for work, leading to zero income earned and zero tax revenue.
**Tasks:**
**a. Find \( f(30) \).**
\( f(30) = \) [Input field]
(Round to the nearest integer as needed.)
**Interpret your result. Choose the correct answer below.**
- A. When the tax rate is 65%, $300 billion in tax revenue is generated.
- B. If the tax rate increases to 85%, an additional $300 billion in revenue is generated.
- C. When the tax rate is 30%, $700 billion in tax revenue is generated.
- D. If the tax rate increases 30%, an additional $700 billion in revenue is generated.
**Identify the solution as a point on the graph. Choose the correct graph below.**
- Option A: (Graph depicting a certain point)
- Option B: (Graph depicting a certain point)
- Option C: (Graph depicting a certain point)
- Option D: (Graph depicting a certain point)
**b. Rewrite the function using long division to perform:**
\[ \frac{110x - 11,000}{x - 140} \]
(Simplify your answer. If there is a remainder, type your answer as \( \text{quotient} + \frac{\text{remainder}}{\text{divisor}} \).)
Then use this new form of the function to find \( f(30) \).
\( f(30) = \) [Input field]
(Round to the nearest integer as needed.)
**c. Is \( f(x) \) a polynomial function? Explain your answer. Choose the correct answer below.**
- Yes, it is a polynomial function because the numerator is not fully factored.
- No, it is not a polynomial function because it cannot be written in the form \( a_nx^n + a_{n-1}x^{n-1} + \
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