Question 212352This question is from textbook
: I am looking for help in solving a question from a text concerning the equilibrium point of the problem.
Here is the problem.
Supply and Demand. The supply and demand for the sale of stereos by Sound Ideas are given by S(x)=e^x and D(x)=162,755e^-x, where S(x) is the price at which the company is willing to supply x stereos and D(x) is the demand price for a quantity of x stereos. Find the equilibrium point.
I understand that this is the point that when graphed would be the intersection. My problem is setting up the problem as an equation and then solving it. I thought it would be e^x= 162,755e^-x but I am totally confused on how to treat the e, and how do I solve for x?
This question is from textbook
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Comment: You are correct when you equate Cost and Demand to determine
the equilibrium point.
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Comment: "e" is the irrational number 2.718281828459.....
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e^x= 162,755e^-x
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Multiply both sides by e^x to get:
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e^(2x) = 162,755
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Take the natural log of both sides to get:
2x = ln(162,755)
2x = 12
x = 6
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Cheers,
Stan H.
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