document.write( "Question 134605: Write a power Function of the form y=ab^x whose graph passes through the given points: (4,3) (9,4.5) \n" ); document.write( "

Algebra.Com's Answer #98470 by vleith(2983) $\"\"$ $\"About$

You can put this solution on YOUR website!
Use Logs
\n" ); document.write( "Given: $\"y=ab%5Ex\"$
\n" ); document.write( " $\"Log%28y%29+=+Log%28a%29+%2B+xLog%28b%29\"$
\n" ); document.write( " $\"Log%28y%29+-+xLog%28b%29+=+Log%28a%29+\"$ \r
\n" ); document.write( "\n" ); document.write( "Sub in both sets of points. Since Log(a) is the same in both equations, we can set them equal to each other.\r
\n" ); document.write( "\n" ); document.write( " $\"Log%283%29+-+4Log%28b%29+=+Log%284.5%29+-+9Log%28b%29\"$
\n" ); document.write( " $\"Log%283%29+-+Log%284.5%29+=+-5Log%28b%29\"$
\n" ); document.write( " $\"%280.477+-+0.653%29%2F-5+=+Lob%28b%29\"$
\n" ); document.write( " $\"0.035218+=+Log%28b%29\"$
\n" ); document.write( " $\"10%5E0.035218+=+b\"$
\n" ); document.write( " $\"1.0845+=+b\"$ \r
\n" ); document.write( "\n" ); document.write( "Now solve for a
\n" ); document.write( " $\"3+=+a%2A%281.0845%29%5E4+\"$
\n" ); document.write( " $\"3%2F1.383+=a\"$ \r
\n" ); document.write( "\n" ); document.write( "Function is:
\n" ); document.write( " $\"y+=+2.169+%2A+1.0845%5Ex+\"$ \r
\n" ); document.write( "\n" ); document.write( "Verify the function by plugging in the given points \n" ); document.write( "

\n" );