document.write( "Question 259028: Write a power function y = axb whose graph passes through (4, 3) and (8, 7).
\n" ); document.write( "Round all answers to two decimal places. \n" ); document.write( "

Algebra.Com's Answer #190717 by drk(1908) $\"\"$ $\"About$

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Our power function is
\n" ); document.write( "(i) $\"y+=+ax%5Eb\"$
\n" ); document.write( "using (4,3), we get
\n" ); document.write( "(ii) $\"3+=+a%2A4%5Eb\"$
\n" ); document.write( "using (8,7), we get
\n" ); document.write( "(iii) $\"7+=+a%2A8%5Eb\"$
\n" ); document.write( "solving (ii) for a, we get
\n" ); document.write( "(iv) $\"a+=+3%2F%284%5Eb%29\"$
\n" ); document.write( "substituting (iv) into (iii) we get
\n" ); document.write( "(v) $\"7+=+%283%2F%284%5Eb%29%29%2A8%5Eb\"$
\n" ); document.write( "which can be simplified to
\n" ); document.write( "(vi) $\"2.333333+=+2%5Eb\"$
\n" ); document.write( "solving for b, we get
\n" ); document.write( "b = 1.2224
\n" ); document.write( "Now substituting this into (iv), we can get a as
\n" ); document.write( "a = .5510
\n" ); document.write( "So, our power function becomes
\n" ); document.write( " $\"y+=+.55%2Ax%5E%281.22%29\"$ \n" ); document.write( "

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