document.write( "Question 961247: write an exponential function in $\"y=ab%5Ex\"$ passing through the points (2,1)(5,16) \n" ); document.write( "

Algebra.Com's Answer #587431 by stanbon(75887) $\"\"$ $\"About$

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write an exponential function in $\"y=ab%5Ex\"$ passing through the points (2,1)(5,16)
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\n" ); document.write( "Solve for \"a\" and \"b\"::
\n" ); document.write( "y = ab^x
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\n" ); document.write( "Using (2,1) you get: 1 = ab^2
\n" ); document.write( "Using (5,16) you get: 16 = ab^5
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\n" ); document.write( "Dividing the bottom eq. by the top eq. you get:
\n" ); document.write( "16 = b^3
\n" ); document.write( "----
\n" ); document.write( "Then b = 2^4/3
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\n" ); document.write( "Solve for \"a\" by substituting for \"b\"::
\n" ); document.write( "1 = a*(2^(4/3)]^2
\n" ); document.write( "1 = a*(2^(8/3))
\n" ); document.write( "a = 2^(-8/3)
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\n" ); document.write( "Ans: y = (2^(-8/3))*(2^(4x/3))
\n" ); document.write( "y = 2^[(-8/3)+(4x/3)]
\n" ); document.write( "y = 2^((4x-8)/3)
\n" ); document.write( "y = 2^[4(x-2)/3]
\n" ); document.write( "y = 16^[(x-2)/3]
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H. \n" ); document.write( "

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