Explanation Given information: Demand of product if p is the price, q = 5000 e − 0.08 p Formula used: Derivative of an exponential function, d d x e k x = k e k x Product rule of derivatives, d d x ( p ⋅ q ) = p q ′ + p ′ q Calculation: Consider the demand function q = 5000 e − 0.08 p . Since the price of a product is $ 10 . Thus, in order to calculate the revenue substitute p = 10 into q = 5000 e − 0.08 p . q ( p ) = 5000 e − 0.08 p q ( 10 ) = 5000 e − 0.08 ( 10 ) = 2250 Thus, the demand is 2250 . Since the revenue is given by Revenue = p ⋅ q ( p ) . Thus, Revenue = p ⋅ q ( p ) = 10 ⋅ 2250 = $ 22500 Further the derivative of the revenue with respect to price

Applied Calculus, 6e WileyPLUS + Loose-leaf

6th Edition

ISBN: 9781119408901

Author: Deborah Hughes-Hallett, Andrew M. Gleason, Patti Frazer Lock, Daniel E. Flath

Publisher: Wiley (WileyPLUS Products)

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Chapter 3.4, Problem 43P

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The revenue and the derivative of the revenue with respect to the price when the price is $10. Mention the interpretation of the answer in economic terms.

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Chapter 3.4, Problem 42P

Chapter 3.4, Problem 44P

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Chapter 3 Solutions

Applied Calculus, 6e WileyPLUS + Loose-leaf

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The revenue and the derivative of the revenue with respect to the price when the price is $ 10 . Mention the interpretation of the answer in economic terms.

Solution Summary: The author explains how to calculate the revenue and derivative of revenue with respect to the price when p is 10.

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To calculate:

The revenue and the derivative of the revenue with respect to the price when the price is $10. Mention the interpretation of the answer in economic terms.

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Chapter 3 Solutions

The revenue and the derivative of the revenue with respect to the price when the price is $ 10 . Mention the interpretation of the answer in economic terms.

Solution Summary: The author explains how to calculate the revenue and derivative of revenue with respect to the price when p is 10.

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To calculate: The revenue and the derivative of the revenue with respect to the price when the price is $10. Mention the interpretation of the answer in economic terms.

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Chapter 3 Solutions

To calculate:

The revenue and the derivative of the revenue with respect to the price when the price is $10. Mention the interpretation of the answer in economic terms.