document.write( "Question 1160114: If f(x) is an exponential function where f(1)=10 and f(6.5)=90, then find the value of f(1.5), to the nearest hundred.
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Algebra.Com's Answer #783268 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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If f(x) is an exponential function where f(1)=10 and f(6.5)=90, then find the value of f(1.5), to the nearest hundred.
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\n" ); document.write( "Using the form a*b^x = y
\n" ); document.write( "x=1, y=10
\n" ); document.write( " $\"a%2Ab%5E1+=+10\"$
\n" ); document.write( "ab = 10
\n" ); document.write( "a = 10/b
\n" ); document.write( ":
\n" ); document.write( "x=6.5, y=90
\n" ); document.write( " $\"a%2Ab%5E6.5+=+90\"$
\n" ); document.write( "replace a with 10/b
\n" ); document.write( " $\"10%2Fb\"$ * $\"b%5E6.5+=+90\"$
\n" ); document.write( "10* $\"b%5E5.5+=+90\"$
\n" ); document.write( "divide both sides by 10
\n" ); document.write( " $\"b%5E5.5+=+9\"$
\n" ); document.write( "using natural logs
\n" ); document.write( "5.5*ln(b) = ln(9)
\n" ); document.write( "ln(b) = $\"ln%289%29%2F5.5\"$
\n" ); document.write( "using your calc
\n" ); document.write( "ln(b) = .3995
\n" ); document.write( "b = 1.491
\n" ); document.write( "find a
\n" ); document.write( "a = 10/1.491
\n" ); document.write( "a = 6.707
\n" ); document.write( "the equation
\n" ); document.write( "f(x) = $\"6.707%2A1.491%5Ex\"$
\n" ); document.write( ":
\n" ); document.write( "\"find the value of f(1.5), to the nearest hundred.
\n" ); document.write( "f(x) = $\"6.707%2A1.491%5E1.5\"$
\n" ); document.write( "using your calc
\n" ); document.write( "f(1.5) = 12.21
\n" ); document.write( ":
\n" ); document.write( "looks like this
\n" ); document.write( " $\"+graph%28+300%2C+200%2C+-4%2C+10%2C+-10%2C+100%2C+6.707%2A1.491%5Ex%2C+12.21%2C+90%29+\"$
\n" ); document.write( "green line is 12.21, blue line is 90 \n" ); document.write( "

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