document.write( "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. \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #217312 by CharlesG2(834)\"\" \"About 
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. \r
\n" ); document.write( "\n" ); document.write( "set the equations equal to each other and solve for x\r
\n" ); document.write( "\n" ); document.write( "e^x = 162755 * e^(-x)
\n" ); document.write( "ln (e^x) = ln (162755 * e^(-x))
\n" ); document.write( "e^x = y --> ln y = x, e is the base of natural logarithms (ln)
\n" ); document.write( "ln e^x = x
\n" ); document.write( "ln (mn) = ln m + ln n
\n" ); document.write( "x = ln 162755 + ln e^(-x)
\n" ); document.write( "x = ln 162755 - x
\n" ); document.write( "2x = ln 162755
\n" ); document.write( "2x = approximately 12
\n" ); document.write( "x = approx. 6
\n" ); document.write( "e^6 = approx. 403.43
\n" ); document.write( "162755 * e^(-6) = approx. 403.43
\n" ); document.write( "so 6 stereos\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );