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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Demand The demand function for a product is modeled by

p = 8000 ( 1 5 5 + e 0.002 x ) .

Find the price p (in dollars) of the product when the quantity demanded is (a) x = 1000 units and (b) x = 2500 units. (c) What is the limit of the price as x increases without bound?

(a)

To determine

To calculate: The price p (in dollars) of the product for the demanded quantity of 1000 units, that is x=1000 when the demand function for a product is given by:

p=8000(155+e0.002x)

Explanation

Given Information:

The demanded quantity is 1000 units, that is, x=1000 when the demand function for a product is given by:

p=8000(155+e0.002x)

Calculation:

Consider the demand function, p=8000(155+e0.002x)

Calculate the price at x=1000 units is computed by substituting x=1000 in the demand function as,

p(1000)=8000(155+e0

(b)

To determine

To calculate: The price p (in dollars) of the product for the demanded quantity of 2500 units, that is x=2500 when the demand function for a product is given by:

p=8000(155+e0.002x)

(c)

To determine

To calculate: The limit of the price p when the demanded quantity x increases without any bound and the demand function for a product is given by:

p=8000(155+e0.002x)

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