document.write( "Question 213273: Find the exponential function f(x)= Ca ^x which contains the points (2,45) and (5,1215) \r
\n" ); document.write( "\n" ); document.write( "please show work i would like to learn this process thanks \n" ); document.write( "

Algebra.Com's Answer #161099 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Given:
\n" ); document.write( " $\"f%28x%29+=+Ca%5Ex\"$
\n" ); document.write( "(2,45)
\n" ); document.write( "(5,1215)
\n" ); document.write( "I'll make 2 equations by substituting these values
\n" ); document.write( "(1) $\"45+=+Ca%5E2\"$
\n" ); document.write( "(2) $\"1215+=+Ca%5E5\"$
\n" ); document.write( "Multiply both sides of (1) by $\"a%5E3\"$
\n" ); document.write( "(1) $\"45a%5E3+=+Ca%5E5\"$
\n" ); document.write( "And substituting again,
\n" ); document.write( "(2) $\"1215+=+45a%5E3\"$
\n" ); document.write( " $\"a%5E3+=+1215%2F45\"$
\n" ); document.write( " $\"a%5E3+=+27\"$
\n" ); document.write( " $\"a+=+3\"$
\n" ); document.write( "(1) $\"45+=+Ca%5E2\"$
\n" ); document.write( " $\"45+=+C%2A9\"$
\n" ); document.write( " $\"C+=+5\"$
\n" ); document.write( "The equation is
\n" ); document.write( " $\"f%28x%29+=+5%2A3%5Ex\"$ answer
\n" ); document.write( "check:
\n" ); document.write( " $\"1215+=+5%2A3%5E5\"$
\n" ); document.write( " $\"1215+=+5%2A243\"$
\n" ); document.write( " $\"1215+=+1215\"$
\n" ); document.write( "OK
\n" ); document.write( " $\"45+=+5%2A3%5E2\"$
\n" ); document.write( " $\"45+=+5%2A9\"$
\n" ); document.write( " $\"45+=+45\"$
\n" ); document.write( "OK \n" ); document.write( "

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