Find the Exponential Function (5,7)

$(5, 7)$

To find an exponential function, $f (x) = a^{x}$ , containing the point, set $f (x)$ in the function to the $y$ value $7$ of the point, and set $x$ to the $x$ value $5$ of the point.

$7 = a^{5}$

Solve the equation for $a$ .

Rewrite the equation as $a^{5} = 7$ .

$a^{5} = 7$

Take the 5th root of both sides of the equation to eliminate the exponent on the left side.

$a = \sqrt[5]{7}$

Substitute each value for $a$ back into the function $f (x) = a^{x}$ to find each possible exponential function.

$f (x) = {(\sqrt[5]{7})}^{x}$

Find the Exponential Function (5,7)

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