document.write( "Question 1097432: Find the equation for an exponential function that passes through the pair of points given below. (Round all coefficients to 4 decimal places when necessary.)
\n" ); document.write( "Through (2, 36) and (4, 324) \n" ); document.write( "

Algebra.Com's Answer #711841 by KMST(5328) $\"\"$ $\"About$

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Let the exponential function be
\n" ); document.write( " $\"f%28x%29=A%2Ab%5Ex\"$ , with $\"b%3E0\"$ .
\n" ); document.write( "We know that
\n" ); document.write( " $\"f%282%29=A%2Ab%5E2=36\"$
\n" ); document.write( " $\"f%284%29=A%2Ab%5E4=324\"$
\n" ); document.write( "So,
\n" ); document.write( " $\"A%2Ab%5E4%2F%28A%2Ab%5E2%29=324%2F36\"$ --> $\"b%5E2=9\"$ --> $\"b=3\"$ .
\n" ); document.write( "Substituting the value found for $\"b\"$ into $\"A%2Ab%5E2=36\"$ ,
\n" ); document.write( "we get $\"A%2A3%5E2=36\"$ --> $\"A%2A9=36\"$ --> $\"A=36%2F9\"$ --> $\"A=4\"$ .
\n" ); document.write( "The function is
\n" ); document.write( " $\"highlight%28f%28x%29=4%2A3%5Ex%29\"$ . \n" ); document.write( "

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