Finite Math Examples

$(14, 4)$

Step 1

To find an exponential function, $f (x) = a^{x}$ , containing the point, set $f (x)$ in the function to the $y$ value $4$ of the point, and set $x$ to the $x$ value $14$ of the point.

$4 = a^{14}$

Step 2

Solve the equation for $a$ .

Tap for more steps...

Step 2.1

Rewrite the equation as $a^{14} = 4$ .

$a^{14} = 4$

Step 2.2

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

$a = \pm \sqrt[14]{4}$

Step 2.3

Simplify $\pm \sqrt[14]{4}$ .

Tap for more steps...

Step 2.3.1

Rewrite $4$ as $2^{2}$ .

$a = \pm \sqrt[14]{2^{2}}$

Step 2.3.2

Rewrite $\sqrt[14]{2^{2}}$ as $\sqrt[7]{\sqrt{2^{2}}}$ .

$a = \pm \sqrt[7]{\sqrt{2^{2}}}$

Step 2.3.3

Pull terms out from under the radical, assuming positive real numbers.

$a = \pm \sqrt[7]{2}$

Step 2.4

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

Tap for more steps...

Step 2.4.1

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

$a = \sqrt[7]{2}$

Step 2.4.2

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

$a = - \sqrt[7]{2}$

Step 2.4.3

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

$a = \sqrt[7]{2}, - \sqrt[7]{2}$

Step 3

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

$f (x) = {(\sqrt[7]{2})}^{x}, f (x) = {(- \sqrt[7]{2})}^{x}$