# Math Help - Find an exponential equation in the form f(x) = Pa^x given two points.

1. ## Find an exponential equation in the form f(x) = Pa^x given two points.

If f(0) = 5 and f(6) = 23, using the form f(x) = $Pa^x$, find the value of P, and then find the value of a.

So far, I have:

$f(6) = Pa^6 = 23$
$P = 23/a^6$

Then I try to solve for a:

$f(0) = Pa^0 = 5$

Is this the right way to go about things? If I plug in my value for P I get:

$(23/a^6)*a^0 = 5$
$(23/a^6)*1 = 5$
$(23/a^6)*1 = 5$
$23/5 = a^6$

Is this the right process? Now how do I solve for a?
$log 23/5 = 6 log a$ ??

2. Yes

$a^6 = \frac{23}{5}$

$a = \left(\frac{23}{5}\right)^{\frac16}$