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