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Observe the table:
The ordered pair are .
Find the first differences of -values in the ordered pair.
Since the first differences are not all equal .
Hence the table of values does not represent a linear function.
Find the second differences of -values in the ordered pair.
Since, the second differences are not all equal,
Hence the table of values does not represent a quadratic function.
Find the Ratios of the -values in the ordered pair and compare.
The ratios of successive -values are equal.
Therefore, the table of values can be modeled by an exponential function.
Write an equation for the function.
The equation is in the form of .
The constant ratio is .
Therefore the exponential equation is .
Find the value of .
Let the ordered pair is .
(Exponential equation)
(Substitute in the equation)
(Multiply)
(Divide each sude by )
(Cancel common terms)
Write an equation.
(Substitute in the eqation)
An equation that models the data is .
The table of values represents an exponential function .
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