Question 1090767
Using Differences to Determine the Model

By finding the differences between dependent values, you can determine the degree of the model for data given as ordered pairs.

    If the {{{first}}} difference is the {{{same}}}{{{ value}}}, the model will be {{{linear}}}.
    If the {{{second}}} difference is the same value, the model will be {{{quadratic}}}.
    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.
example:

{{{x}}}|{{{y}}}
{{{0}}}|{{{4}}}
{{{1}}}|{{{12}}}
{{{2}}}|{{{36}}}
{{{3}}}|{{{108}}}
{{{4}}}|{{{324}}}


{{{4}}}..............{{{12}}}.................{{{36}}}...............{{{108}}}................{{{324}}}
..........{{{8}}}.................{{{24}}}..............{{{72}}}................{{{216}}}-> The first differences are not all equal. So, the table of values does not represent a linear function
....................{{{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

 ratio of {{{y}}}- values: 
{{{12/4=3}}}
{{{36/12=3}}}
{{{108/36=3}}}
{{{324/108=3}}}


The equation to represent this data is {{{y=4*3^x}}}

Note that the ratio of values is the same between each set of numbers. This is an {{{exponential}}} equation.