# How do you find the formula of an exponential graph given #f(2)=9/4# and #f(-2)=4/9#?

##### 1 Answer

Sep 1, 2016

#### Explanation:

The exponential function can be expressed in the form:

#f(x) = a*b^x#

where

Note that:

#1 = 9/4*4/9 = f(2)*f(-2) = (a*b^2)*(a*b^(-2)) = a^2*b^2/b^2 = a^2#

Transposing, we find

Then:

#b^2 = 1*b^2 = a*b^2 = f(2) = 9/4#

Hence:

#b = sqrt(9/4) = 3/2#

(We can ignore the possibility of the negative square root since we want

So we can write:

#f(x) = 1*(3/2)^x#

or more simply:

#f(x) = (3/2)^x#

graph{(y-(3/2)^x)((x-2)^2+(y-9/4)^2-0.006)((x+2)^2+(y-4/9)^2-0.006) = 0 [-5.087, 4.913, -0.92, 4.08]}