Finite Math Examples

$(10, 8)$

Step 1

To find an exponential function, $f (x) = a^{x}$ , containing the point, set $f (x)$ in the function to the $y$ value $8$ of the point, and set $x$ to the $x$ value $10$ of the point.

$8 = a^{10}$

Step 2

Solve the equation for $a$ .

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Step 2.1

Rewrite the equation as $a^{10} = 8$ .

$a^{10} = 8$

Step 2.2

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

$a = \pm \sqrt[10]{8}$

Step 2.3

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

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Step 2.3.1

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

$a = \sqrt[10]{8}$

Step 2.3.2

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

$a = - \sqrt[10]{8}$

Step 2.3.3

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

$a = \sqrt[10]{8}, - \sqrt[10]{8}$

Step 3

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

$f (x) = {(\sqrt[10]{8})}^{x}, f (x) = {(- \sqrt[10]{8})}^{x}$