Question 981783
<pre>
Instead of doing your problem, I will do one EXACTLY in every detail like
your problem.  Then you can use it as a model to do yours by:

I will do this one:
</pre>
Find a possible formula for a power function with the properties that 
g(3)=4/3 and g(4)=4/9. 
<pre>
I start by assuming the general power formula for g(x)

{{{g(x)}}}{{{""=""}}}{{{A*B^x}}}

I substitute x=3 and set that equal to 4/3:

{{{g(3)}}}{{{""=""}}}{{{A*B^3}}}{{{""=""}}}{{{4/3}}}

Then I substitute x=4 and set that equal to 4/9:

{{{g(4)}}}{{{""=""}}}{{{A*B^4}}}{{{""=""}}}{{{4/9}}}

Then I divide equals by equals dividing g(4) by g(3)

{{{"g(4)"/"g(3)"}}}{{{""=""}}}{{{(A*B^4)/(A*B^3)}}}{{{""=""}}}{{{(4/9)/(4/3)}}}

        {{{(cross(A)*B^cross(4))/(cross(A)*cross(B^3))}}}{{{""=""}}}{{{12/36}}}

        {{{B}}}{{{""=""}}}{{{1/3}}}

I substitute that in {{{A*B^3}}}{{{""=""}}}{{{4/3}}}

              {{{A*(1/3)^3}}}{{{""=""}}}{{{4/3}}}

              {{{A*(1/27)}}}{{{""=""}}}{{{4/3}}}

I multiply both sides by 27 to clear of fractions:

              {{{A}}}{{{""=""}}}{{{27*expr(4/3)}}}

              {{{A}}}{{{"=""}}}{{{36}}}

Therefore my power function {{{g(x)}}}{{{""=""}}}{{{A*B^x}}} becomes
              
Answer:       {{{g(x)}}}{{{""=""}}}{{{36*(1/3)^x}}}

Now do your problem exactly the same way I did mine.

Edwin</pre>