Question 303145: 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.
Answer by CharlesG2(834)   (Show Source):
You can put this solution on YOUR website! 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.
set the equations equal to each other and solve for x
e^x = 162755 * e^(-x)
ln (e^x) = ln (162755 * e^(-x))
e^x = y --> ln y = x, e is the base of natural logarithms (ln)
ln e^x = x
ln (mn) = ln m + ln n
x = ln 162755 + ln e^(-x)
x = ln 162755 - x
2x = ln 162755
2x = approximately 12
x = approx. 6
e^6 = approx. 403.43
162755 * e^(-6) = approx. 403.43
so 6 stereos
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