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]
