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.