The supply function and demand function for the sale of a certain type of DVD player are given by S(p)=130e0.004p and D(p)=416e−0.002p, 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). This is called the equilibrium price.

p=$193.86 (assuming we are talking about dollars)

Step-by-step explanation:

In order to solve this problem, we must set each function equal to each other, so we end up with the following equation we must solve for p:

So next, we divide both sides of the equation by 130 and by

So we get:

and we simplify, so we get:

which can be further simplified to:

and next, we take the natural logarithm to both sides, so we get:

0.006p=ln(3.2)

and finally we divide both sides of the equation by 0.006 so we get:

and simplify so we get our

p=$193.86  (in the case that p is given in dollars)

for ex: the reciprocal of 3/4 is 4/3. it is the opposite.

reciprocal definition:

a mathematical expression or function so related to another that their product is one; the quantity obtained by dividing the number one by a given quantity.