# Thread: finding an exponential function

1. ## finding an exponential function

Find the exponential function f(x) = Cax whose graph is given.
f(x) = 1

any help with this?

2. Originally Posted by kyleu03
Find the exponential function f(x) = Cax whose graph is given.
f(x) = 1

any help with this?
An exponential equation of this shape will have an equation $f(x)=a(b^{-x})$.

Plugging in the two points gives us:

$2=a(b^{-0})$
$\frac{2}{9}=a(b^{-2})$

Solve this system for $a$ and $b$.

Spoiler:
Solving the first equation give us $a=2$. Plugging into the second equation gives us

$\frac{2}{9}=2(b^{-2})\implies \frac{1}{9}=b^{-2}\implies b=3$.

So the equation of the curve is $f(x)=2(3^{-x})$.