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​, w

Question

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.

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bonexptip 4 years 2021-08-14T09:07:59+00:00 1 Answers 17 views 0

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  1. thongdat2
    0
    2021-08-14T09:09:47+00:00
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    Answer:

    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:

    130e^{0.004p}=416e^{-0.002p}

    So next, we divide both sides of the equation by 130 and by e^{-0.002p}

    So we get:

    \frac{e^{0.004p}}{e^{-0.002p}}=\frac{416}{130}

    and we simplify, so we get:

    e^{0.004p}e^{0.002p}=3.2

    which can be further simplified to:

    e^{0.006p}=3.2

    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:

    p=\frac{ln(3.2)}{0.006}

    and simplify so we get our answer:

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

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