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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336
Textbook Problem

Suppose N is the number of people in the United States who travel by car to another state for a vacation this year when the average price of gasoline is p dollars per gallon. Do you expect dN/dp to be positive or negative? Explain.

To determine

To identify: The sign of dNdp with proper explanation.

Explanation

Given:

N represents the number of persons in the United States travelling by car to another state for vacation when average cost of gasoline is p dollars per gallon this year.

There arise four cases:

Case 1:

The price of the fuel goes up while the number of people also goes up.

In this case, change in price will be positive and change in persons will be positive.

Since ratio of two positive real number is always positive, dNdp will be positive.

Case 2:

The price of the fuel goes up while the number of people also goes down.

In this case, change in price will be positive and change in persons will be negative.

Since ratio of a negative real number with a positive real number is always negative,

dNdp will be negative

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