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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 marginal price for the demand of a product can be modeled by

d p d x = 0.1 e x / 500 where x is the quantity demanded. When the demand is 600 units, the price p is $30.

(a) Find the demand function.

(b) Use a graphing utility to graph the demand function. Does price increase or decrease as demand increases?

(c) Use the zoom and trace features of the graphing utility to find the quantity demanded when the price is $22.

(a)

To determine

To calculate: A demand function, if the marginal price for the demand of product given by

dpdx=0.1ex/500, Where x is the quantity demanded.

Explanation

Given Information:

A demand rate of change can be modeled by

dpdx=0.1ex/500

When demand is 600 units, the price is $30.

Where the quantity demanded (in days) is x.

Formula used:

The exponent rule of integrals:

eu(x)du(x)=eu(x)+C (for n1)

Here, u is function of x.

Calculation:

Consider demand function's rate of change:

dpdx=0.1ex/500

Integrate both sides with respect to x.

dPdxdt=(0.1ex/500)dx+CP(x)=(0.1ex/500)dx+C

Consider the integration:

(0.1ex/500)dx

Rewrite the integration as:

500(0

(b)

To determine

To graph: The demand function p(x)=50ex/500+45.06 and determine price increase or decrease as demand increases.

(c)

To determine

To calculate: The quantity demand when the price is $22.

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