The demand for ceiling fans can be modeled below as D(p) = 25.62(0.996P) thousand ceiling fans where p is the price (in dollars) of a ceiling fan. (a) According to the model, is there a price above which consumers will no longer purchase fans? Explain why or why not. The model is exponential and ---Select--- ✓the horizontal axis. Therefore there ---Select--- above which consumers will not purchase a ceiling fan. (b) Calculate the amount that consumers are willing and able to spend to purchase 17 thousand ceiling fans. (Round your answer to three decimal places.) $ thousand (c) How many fans will consumers purchase when the market price is $100? (Round your answer to three decimal places.) thousand fans (d) Find the consumers' surplus when the market price is $100. (Round your answer to three decimal places.) thousand
The demand for ceiling fans can be modeled below as D(p) = 25.62(0.996P) thousand ceiling fans where p is the price (in dollars) of a ceiling fan. (a) According to the model, is there a price above which consumers will no longer purchase fans? Explain why or why not. The model is exponential and ---Select--- ✓the horizontal axis. Therefore there ---Select--- above which consumers will not purchase a ceiling fan. (b) Calculate the amount that consumers are willing and able to spend to purchase 17 thousand ceiling fans. (Round your answer to three decimal places.) $ thousand (c) How many fans will consumers purchase when the market price is $100? (Round your answer to three decimal places.) thousand fans (d) Find the consumers' surplus when the market price is $100. (Round your answer to three decimal places.) thousand
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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![### Demand for Ceiling Fans: An Exponential Model
The demand for ceiling fans is modeled by the following equation:
\[ D(p) = 25.62(0.996^p) \text{ thousand ceiling fans} \]
where \( p \) represents the price (in dollars) of a ceiling fan.
#### (a) Price Threshold for Ceasing Purchases
**Question:** According to the model, is there a price above which consumers will no longer purchase fans? Explain why or why not.
**Model Explanation:**
The model is exponential and \( \lim_{p \to \infty} D(p) = 0 \). Therefore, there **is not** a specific price above which consumers will not purchase a ceiling fan. Consumers will always purchase fans, just in decreasing quantities as the price increases indefinitely.
#### (b) Willingness to Spend
**Question:** Calculate the amount that consumers are willing and able to spend to purchase 17 thousand ceiling fans. (Round your answer to three decimal places.)
**Solution:**
\[ \text{\$} \_ \_ \_.\_ \_ \_ \text{ thousand} \]
#### (c) Purchase Quantity at Specific Market Price
**Question:** How many fans will consumers purchase when the market price is $100? (Round your answer to three decimal places.)
**Solution:**
\[ \text{\_ \_ \_.\_ \_ \_ \text{ thousand fans}} \]
#### (d) Consumers' Surplus
**Question:** Find the consumers' surplus when the market price is $100. (Round your answer to three decimal places.)
**Solution:**
\[ \text{\$} \_ \_ \_.\_ \_ \_ \text{ thousand} \]
This model provides a framework for understanding consumer behavior and how demand changes with pricing. Further exercises can help in applying this model to real-world scenarios and enhancing conceptual understanding.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbcfa3f98-eb44-4f4d-86d7-8c297108b84f%2Fb3db5d8b-4b10-41e8-910b-50454f420cb6%2Fac2ar9r_processed.png&w=3840&q=75)
Transcribed Image Text:### Demand for Ceiling Fans: An Exponential Model
The demand for ceiling fans is modeled by the following equation:
\[ D(p) = 25.62(0.996^p) \text{ thousand ceiling fans} \]
where \( p \) represents the price (in dollars) of a ceiling fan.
#### (a) Price Threshold for Ceasing Purchases
**Question:** According to the model, is there a price above which consumers will no longer purchase fans? Explain why or why not.
**Model Explanation:**
The model is exponential and \( \lim_{p \to \infty} D(p) = 0 \). Therefore, there **is not** a specific price above which consumers will not purchase a ceiling fan. Consumers will always purchase fans, just in decreasing quantities as the price increases indefinitely.
#### (b) Willingness to Spend
**Question:** Calculate the amount that consumers are willing and able to spend to purchase 17 thousand ceiling fans. (Round your answer to three decimal places.)
**Solution:**
\[ \text{\$} \_ \_ \_.\_ \_ \_ \text{ thousand} \]
#### (c) Purchase Quantity at Specific Market Price
**Question:** How many fans will consumers purchase when the market price is $100? (Round your answer to three decimal places.)
**Solution:**
\[ \text{\_ \_ \_.\_ \_ \_ \text{ thousand fans}} \]
#### (d) Consumers' Surplus
**Question:** Find the consumers' surplus when the market price is $100. (Round your answer to three decimal places.)
**Solution:**
\[ \text{\$} \_ \_ \_.\_ \_ \_ \text{ thousand} \]
This model provides a framework for understanding consumer behavior and how demand changes with pricing. Further exercises can help in applying this model to real-world scenarios and enhancing conceptual understanding.
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