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Find the price-demand equation for a particular brand television when the demand is 20 TVs per week at $150 per TV, given that the marginal price-demand function, p′(x), for x number of TVs per week, is given as p′(x)=−0.5e−0.01x. If 100 TVs are sold per week, what should the price be? Round your answer to the nearest hundredth and do not include a dollar sign in your answer.

Sagot :

okpalawalter8

Answer:

~[tex]150=50e^{-0.01()20}[/tex]

~[tex]p(100)=\$127.7[/tex]

Step-by-step explanation:

From the question we are told that:

Price of 20TVs per week [tex]P_{20}=\$150[/tex]

Marginal price-demand function [tex]p'(x)=-0.5e-0.01x[/tex]

Generally the The Marginal price function is mathematically given by

  [tex]p'(x)=-0.5e^{-0.01x}[/tex]  

  [tex]p(x)=\int-0.5e^{-0.01x}[/tex]  

  [tex]p(x)=50e^{-0.001x}+C[/tex]  

Therefore the equation when the demand is 20 TVs per week at $150 per TV

[tex]150=50e^{-0.01()20}[/tex]

Giving

[tex]p(x)=50e^{-0.01x}+150-50e^{-0.01(20)}[/tex]

Therefore the Price when the demand is 100 TVs per week

[tex]p(100)=50e^{-0.01(100)}+150-50e^{-0.01(20)}[/tex]

[tex]p(100)=\$127.7[/tex]

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