Question

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.

Answer 1

Answer:

~$150=50e^{-0.01()20}$

~$p(100)=\ 127.7$

Step-by-step explanation:

From the question we are told that:

Price of 20TVs per week $P_{20}=\ 150$

Marginal price-demand function $p'(x)=-0.5e-0.01x$

Generally the The Marginal price function is mathematically given by

  $p'(x)=-0.5e^{-0.01x}$  

  $p(x)=\int-0.5e^{-0.01x}$  

  $p(x)=50e^{-0.001x}+C$  

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

$150=50e^{-0.01()20}$

Giving

$p(x)=50e^{-0.01x}+150-50e^{-0.01(20)}$

Therefore the Price when the demand is 100 TVs per week

$p(100)=50e^{-0.01(100)}+150-50e^{-0.01(20)}$

$p(100)=\ 127.7$