Question 191371
{{{y=ab^x}}} Start with the given equation.



{{{12=ab^(1)}}} Plug in {{{x=1}}} and {{{y=12}}}.  These are the x and y coordinates to the point (1,12)



{{{12=ab}}} Simplify



{{{12/a=b}}} Divide both sides by "a".



{{{b=12/a}}} Rearrange the equation



------------------------


{{{y=ab^x}}} Go back to the given equation.



{{{36=ab^(2)}}} Plug in {{{x=2}}} and {{{y=36}}}. These are the x and y coordinates to the point (2,36)


 
{{{36=a(12/a)^(2)}}} Plug in {{{b=12/a}}} 



{{{36=a(144/a^2)}}} Square {{{12/a}}} to get {{{144/a^2}}}



{{{36=(144a)/(a^2)}}} Multiply



{{{36=144/a}}} Reduce



{{{36a=144}}} Multiply both sides by "a".



{{{a=144/36}}} Divide both sides by 36.



{{{a=4}}} Reduce


-----------------------


{{{b=12/a}}} Go back to the first isolated equation



{{{b=12/4}}} Plug in {{{a=4}}}



{{{b=3}}} Reduce



So the exponential equation is {{{y=4*3^x}}}