Find the Exponential Function (2,64)

$(2, 64)$

Step 1

To find an exponential function, $f (x) = a^{x}$ , containing the point, set $f (x)$ in the function to the $y$ value $64$ of the point, and set $x$ to the $x$ value $2$ of the point.

$64 = a^{2}$

Step 2

Solve the equation for $a$ .

Rewrite the equation as $a^{2} = 64$ .

$a^{2} = 64$

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

$a = \pm \sqrt{64}$

Simplify $\pm \sqrt{64}$ .

Rewrite $64$ as $8^{2}$ .

$a = \pm \sqrt{8^{2}}$

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

$a = \pm 8$

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.

$a = 8$

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

$a = - 8$

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

$a = 8, - 8$

Step 3

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

$f (x) = {(8)}^{x}, f (x) = {(- 8)}^{x}$

Find the Exponential Function (2,64)

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