Explanation Given: A cell phone that is offered at a price of P dollars per month attracts C customers, where C ( P ) is a linear demand function for $ 100 ≤ P ≤ $ 500 and C ( 100 ) = 1 , 000 , 000 , C ( 500 ) = 100 , 000 . Concept Used: Demand function : - it is the mathematical expression of the relationship between the quantity of services or goods that is demanded and changes in a number of economic factors, such as its own price. The quantity demanded is the dependent variable the other factors and independent variables the other factors and independent variables. In equation form: Q d = a − b P Where Q d = quantity demanded a = intercept of the equation b = slope of the function Here, intercept − gives the quantity demanded when price is zero Slope − gives the unit change in quantity demanded for every unit change in price: b = Δ Q d Δ P Calculation: As per the given problem C ( 100 ) = 1 , 000 , 000 Where, Q d 1 = 1 , 000 , 000 , P 1 = 100 C ( 500 ) = 100 , 000 Where, Q d 2 = 1 , 00 , 000 , P 1 = 500 So, by the demand function: To determine (b) Find the slope of the graph of C ( P ) . To determine (c) To find the decrease in the number of customers for each increase of $ 100 in the price.

Loose-Leaf Version for Calculus: Early Transcendentals Single Variable

4th Edition

ISBN: 9781319312886

Author: Rogawski, Jon, Adams, Colin, FRANZOSA, Robert

Publisher: W. H. Freeman

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Question

Chapter 1, Problem 29CRE

To determine

(a)

Find the demand function C(P).

To determine

(b)

Find the slope of the graph of C(P).

To determine

(c)

To find the decrease in the number of customers for each increase of $100 in the price.

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Chapter 1, Problem 28CRE

Chapter 1, Problem 30CRE

Chapter 1 Solutions

Loose-Leaf Version for Calculus: Early Transcendentals Single Variable

Ch. 1.1 - Prob. 1PQ Ch. 1.1 - Prob. 2PQ Ch. 1.1 - Prob. 3PQ Ch. 1.1 - Prob. 4PQ Ch. 1.1 - Prob. 5PQ Ch. 1.1 - Prob. 6PQ Ch. 1.1 - Prob. 7PQ Ch. 1.1 - Prob. 8PQ Ch. 1.1 - Prob. 9PQ Ch. 1.1 - Prob. 10PQ

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(a) Find the demand function C ( P ) .

Solution Summary: The author explains the demand function, which is the mathematical expression of the relationship between the quantity of services or goods demanded and changes in a number of economic factors, such as its own price.

Concept explainers

Videos

(a)

Find the demand function C(P).

(b)

Find the slope of the graph of C(P).

(c)

To find the decrease in the number of customers for each increase of $100 in the price.

Want to see the full answer?

Chapter 1 Solutions

(a) Find the demand function C ( P ) .

Solution Summary: The author explains the demand function, which is the mathematical expression of the relationship between the quantity of services or goods demanded and changes in a number of economic factors, such as its own price.

Concept explainers

Videos

(a) Find the demand function C(P).

(b) Find the slope of the graph of C(P).

(c) To find the decrease in the number of customers for each increase of $100 in the price.

Want to see the full answer?

Chapter 1 Solutions

(a)

Find the demand function C(P).

(b)

Find the slope of the graph of C(P).

(c)

To find the decrease in the number of customers for each increase of $100 in the price.