# How do you find formulas for the exponential functions satisfying the given conditions f(3)=-3/8 and f(-2)=-12?

##### 1 Answer

#### Explanation:

Suppose we have an exponential function of the form

Given our conditions, we get the system

Multiplying the first equation by

Thus, equating the two, we have

Multiplying by

Taking the natural log of both sides, we find

Note, then, that

Now we can substitute this back into a prior equation, say,

#=-12/4#

#=-3#

Thus we get our full equation as

Checking we find that

and

as desired.