College Math 1314

Question

The supply function and demand function for the sale of a certain type of DVD player are given by S(p)=140e^0.004p and D(p)=490e ^ -0.002p, where S(p) is the number of DVD players that the company is willing to sell at a 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). This is called equilibrium price

Answer 1

S(p) = D(p)

140e^.004p = 490e^-.002p multiply by e^.002p, divide by 140

e^.004p(e^.002) = 490/140 = 7/2 add the exponents

e^.006p = 3.5 take natural logs of both sides

.006p = ln3.5 divide by .006

p = ln3.5/.006 = about 183.10

equilibrium price = $183.10