Find the Exponential Function (3,2)

$(3, 2)$

Step 1

To find an exponential function, $f (x) = a^{x}$ , containing the point, set $f (x)$ in the function to the $y$ value $2$ of the point, and set $x$ to the $x$ value $3$ of the point.

$2 = a^{3}$

Step 2

Solve the equation for $a$ .

Rewrite the equation as $a^{3} = 2$ .

$a^{3} = 2$

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

$a = \sqrt[3]{2}$

Step 3

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

$f (x) = {(\sqrt[3]{2})}^{x}$

Find the Exponential Function (3,2)

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