Finite Math Examples

$(45, 85)$

Step 1

To find an exponential function, $f (x) = a^{x}$ , containing the point, set $f (x)$ in the function to the $y$ value $85$ of the point, and set $x$ to the $x$ value $45$ of the point.

$85 = a^{45}$

Step 2

Solve the equation for $a$ .

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Step 2.1

Rewrite the equation as $a^{45} = 85$ .

$a^{45} = 85$

Step 2.2

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

$a = \sqrt[45]{85}$

Step 3

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

$f (x) = {(\sqrt[45]{85})}^{x}$