(a) Explanation Given Information: The demand function for a product is given by: p = 12 , 000 ( 1 − 3 3 + e − 0.001 x ) Where, p is the price of the product in dollars and x is the number of units sold. Formula used: The inverse property of logarithms for the expression ln e x is ln e x = x . The property of logarithms for the expression ln ( x y ) is ln ( x y ) = ln x − ln y where x and y are real numbers greater than 0 . Calculation: Consider the demand function, p = 12 , 000 ( 1 − 3 3 + e − 0.001 x ) Calculate the number of units sold if the price of the product is $ 500 by substituting p = 500 in the demand function as, 500 = 12 , 000 ( 1 − 3 3 + e − 0.001 x ) Divide the both sides by 12 , 000 as, 500 12 , 000 = 12 , 000 ( 1 − 3 3 + e − 0.001 x ) 12 , 000 1 − 3 3 + e − 0.001 x = 1 24 Subtract 1 from both sides as, 1 − 3 3 + e − 0.001 x − 1 = 1 24 − 1 − 3 3 + e − 0.001 x = 1 − 24 24 − 3 3 + e − 0.001 x = − 23 24 Cancel the minus sign from the both sides and simplify as, 3 3 + e − 0.001 x = 23 24 Multiply both sides by 24 ( 3 + e − 0.001 x ) as, 3 3 + e − 0 (b) To determine To calculate: The number of units sold if the price of the product is $ 1600 , that is p = $ 1600 when the demand function for a product is given by: p = 12 , 000 ( 1 − 3 3 + e − 0.001 x ) Where, p is the price of the product in dollars and x is the number of units sold. Also verify the result using technology.

CALCULUS APPLIED APPROACH >PRINT UGRADE<

10th Edition

ISBN: 9780357667231

Author: Larson

Publisher: CENGAGE L

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Question

Chapter 4.4, Problem 86E

(a)

To determine

To calculate: The number of units sold if the price of the product is $500, that is p=$500 when the demand function for a product is given by:

p=12,000(1−33+e−0.001x)

Where, p is the price of the product in dollars and x is the number of units sold. Also verify the result using technology.

(b)

To determine

To calculate: The number of units sold if the price of the product is $1600, that is p=$1600 when the demand function for a product is given by:

p=12,000(1−33+e−0.001x)

Where, p is the price of the product in dollars and x is the number of units sold. Also verify the result using technology.

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Chapter 4.4, Problem 85E

Chapter 4.4, Problem 87E

Chapter 4 Solutions

CALCULUS APPLIED APPROACH >PRINT UGRADE<

Ch. 4.1 - Use the properties of exponents to simplify each...Ch. 4.1 - Use the properties of exponents to simplify each...Ch. 4.1 - Use the formula for the ratio of carbon isotopes...Ch. 4.1 - Prob. 4CP Ch. 4.1 - Prob. 5CP Ch. 4.1 - Prob. 1SWU Ch. 4.1 - Prob. 2SWU Ch. 4.1 - Prob. 3SWU Ch. 4.1 - Prob. 4SWU Ch. 4.1 - Prob. 5SWU

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The number of units sold if the price of the product is $ 500 , that is p = $ 500 when the demand function for a product is given by: p = 12 , 000 ( 1 − 3 3 + e − 0.001 x ) Where, p is the price of the product in dollars and x is the number of units sold. Also verify the result using technology.

Solution Summary: The author explains how to calculate the number of units sold if the price of the product is 500.

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To calculate: The number of units sold if the price of the product is $500, that is p=$500 when the demand function for a product is given by:

p=12,000(1−33+e−0.001x)

Where, p is the price of the product in dollars and x is the number of units sold. Also verify the result using technology.

To calculate: The number of units sold if the price of the product is $1600, that is p=$1600 when the demand function for a product is given by:

p=12,000(1−33+e−0.001x)

Where, p is the price of the product in dollars and x is the number of units sold. Also verify the result using technology.

Want to see the full answer?

Chapter 4 Solutions

Solution Summary: The author explains how to calculate the number of units sold if the price of the product is 500.

Concept explainers

Videos

To calculate: The number of units sold if the price of the product is $500, that is p=$500 when the demand function for a product is given by: p=12,000(1−33+e−0.001x) Where, p is the price of the product in dollars and x is the number of units sold. Also verify the result using technology.

To calculate: The number of units sold if the price of the product is $1600, that is p=$1600 when the demand function for a product is given by: p=12,000(1−33+e−0.001x) Where, p is the price of the product in dollars and x is the number of units sold. Also verify the result using technology.

Want to see the full answer?

Chapter 4 Solutions

To calculate: The number of units sold if the price of the product is $500, that is p=$500 when the demand function for a product is given by:

p=12,000(1−33+e−0.001x)

Where, p is the price of the product in dollars and x is the number of units sold. Also verify the result using technology.

To calculate: The number of units sold if the price of the product is $1600, that is p=$1600 when the demand function for a product is given by:

p=12,000(1−33+e−0.001x)

Where, p is the price of the product in dollars and x is the number of units sold. Also verify the result using technology.