Algebra help-No idea

Question

The supply function and demand function for the sale of certain type of DVD player are given by S(p)=150e^0.005p and D(p)=480e^-0.003p, where S(p) is the number of DVD players that the company is willing to sell at price p and D(p) is the quantity that the public is willing to buy at price p. Find p such that D(p)=S(p). The equilibrium price.

Answer 1

If you want D(p) = S(p) then set the 2 expressions equal to each other and solve for p  

 

480e^-0.003p = 150e^0.005p 

 

Multiply both sides by e^0.003p and use the addition law for exponents (e^ae^b = e^a+b) to get 

 

480 = 150e^0.008p  

3.2 = e^0.008p

 

Take the natural logarithm ln of both sides 

 

ln(3.2) = 0.008p

p = ln(3.2)/0.008 = 145.39  

 

Check:  S(145.39) = 150e^0.005*145.39 = 310.3

            D(145.39) = 480e^{-0.003*145.39} = 310.3