What is the exponential growth formula?

The exponential growth formula is:
##y = a * b^x##
For example, if you have two coordinates, (3, 27) and (6, 729).
You’d first plug the numbers into the equation and set them both equal to a.
##27 = a *b^3## and ##729 = a *b^6##
##a=27/b^3## and ##a=729/b^6##
Then, since they’re both equal to a, you can set them equal to each other and solve for b.
##27/b^3 = 729/b^6## now you do a cross-multiplication:
##27*b^6=729*b^3## divide by ##b^3##
##27*b^3=729 ->b^3=729/27=27##
##b=root 3 27=3##
Then, put b back into the equation and find a:
##27 = a *3^3->27=a*27->a=1##
The complete equation is then ##y=1*3^x=3^x##
Check your answer with the other equation:
##3^6=729## = correct