Find the Exponential Function (4,15)

$(4, 15)$

Step 1

To find an exponential function, $f (x) = a^{x}$ , containing the point, set $f (x)$ in the function to the $y$ value $15$ of the point, and set $x$ to the $x$ value $4$ of the point.

$15 = a^{4}$

Step 2

Solve the equation for $a$ .

Rewrite the equation as $a^{4} = 15$ .

$a^{4} = 15$

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

$a = \pm \sqrt[4]{15}$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$a = \sqrt[4]{15}$

Next, use the negative value of the $\pm$ to find the second solution.

$a = - \sqrt[4]{15}$

The complete solution is the result of both the positive and negative portions of the solution.

$a = \sqrt[4]{15}, - \sqrt[4]{15}$

Step 3

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

$f (x) = {(\sqrt[4]{15})}^{x}, f (x) = {(- \sqrt[4]{15})}^{x}$

Find the Exponential Function (4,15)

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