Question 1097432
Let the exponential function be
{{{f(x)=A*b^x}}} , with {{{b>0}}} .
We know that
{{{f(2)=A*b^2=36}}}
{{{f(4)=A*b^4=324}}}
So,
{{{A*b^4/(A*b^2)=324/36}}} --> {{{b^2=9}}} --> {{{b=3}}} .
Substituting the value found for {{{b}}} into {{{A*b^2=36}}} ,
we get {{{A*3^2=36}}} --> {{{A*9=36}}} --> {{{A=36/9}}} --> {{{A=4}}} .
The function is
{{{highlight(f(x)=4*3^x)}}} .