$\"\"$

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Observe the table:

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The ordered pair are $\"\"$ .

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Find the first differences of $\"\"$ -values in the ordered pair.

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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The first differences are not all equal .

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Hence the table of values does not represent a linear function.

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Find the second differences of $\"\"$ -values in the ordered pair.

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$\"\"$

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$\"\"$

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$\"\"$

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Since, the second differences are not all equal,

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Hence the table of values does not represent a quadratic function.

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Find the ratios of the $\"\"$ -values in the ordered pair and compare.

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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The ratios of successive $\"\"$ -values are equal.

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Therefore, the table of values can be modeled by an exponential function.

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$\"\"$

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Write an equation for the function.

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The equation is in the form of $\"\"$ .

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The constant ratio is $\"\"$ .

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Therefore the exponential equation is $\"\"$ .

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Find the value of $\"\"$ .

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Let the ordered pair is $\"\"$ .

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$\"\"$ (Formula for equation)

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$\"\"$ (Substitute $\"\"$ in the formula)

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$\"\"$ (Multiply)

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$\"\"$ (Divide each side by $\"\"$ )

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$\"\"$ (Cancel common terms)

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Write an equation.

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$\"\"$ (Substitute $\"\"$ in the formula)

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An equation that models the data is $\"\"$ .

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$\"\"$

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The table of values represents an exponential function $\"\"$ .