document.write( "Question 1090767: Explain how you can use first and second differences to identify an exponential function. \n" ); document.write( "

Algebra.Com's Answer #705310 by MathLover1(20850) $\"\"$ $\"About$

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Using Differences to Determine the Model\r
\n" ); document.write( "\n" ); document.write( "By finding the differences between dependent values, you can determine the degree of the model for data given as ordered pairs.\r
\n" ); document.write( "\n" ); document.write( " If the $\"first\"$ difference is the $\"same\"$ $\"+value\"$ , the model will be $\"linear\"$ .
\n" ); document.write( " If the $\"second\"$ difference is the same value, the model will be $\"quadratic\"$ .
\n" ); document.write( " If the $\"number+\"$ of $\"times\"$ the difference has been taken $\"before\"$ finding $\"repeated\"$ values $\"+exceeds\"$ $\"five\"$ (common multiplication pattern), the model may be $\"exponential\"$ or some other special equation. $\"y+\"$ changes more quickly than $\"x\"$ , and you never see the same $\"y\"$ value twice.
\n" ); document.write( "example:\r
\n" ); document.write( "\n" ); document.write( " $\"x\"$ | $\"y\"$
\n" ); document.write( " $\"0\"$ | $\"4\"$
\n" ); document.write( " $\"1\"$ | $\"12\"$
\n" ); document.write( " $\"2\"$ | $\"36\"$
\n" ); document.write( " $\"3\"$ | $\"108\"$
\n" ); document.write( " $\"4\"$ | $\"324\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"4\"$ .............. $\"12\"$ ................. $\"36\"$ ............... $\"108\"$ ................ $\"324\"$
\n" ); document.write( ".......... $\"8\"$ ................. $\"24\"$ .............. $\"72\"$ ................ $\"216\"$ -> The first differences are not all equal. So, the table of values does not represent a linear function
\n" ); document.write( ".................... $\"16\"$ ............. $\"56\"$ ................ $\"160\"$ -> The second differences are not all equal. So, the table of values does not represent a quadratic function. Find the ratios of the y-values and compare\r
\n" ); document.write( "\n" ); document.write( " ratio of $\"y\"$ - values:
\n" ); document.write( " $\"12%2F4=3\"$
\n" ); document.write( " $\"36%2F12=3\"$
\n" ); document.write( " $\"108%2F36=3\"$
\n" ); document.write( " $\"324%2F108=3\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The equation to represent this data is $\"y=4%2A3%5Ex\"$ \r
\n" ); document.write( "\n" ); document.write( "Note that the ratio of values is the same between each set of numbers. This is an $\"exponential\"$ equation.\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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