Find the exponential function that contains the point (1,27) and (5,2187). This is hard for me.

We have the form

y = ab^x

And we know that

27 = ab^1   ⇒  27 = ab   ⇒  27/b  =  a     (1)

2187  = ab^5        (2)

Sub  (1)  into (2)  for  a

2187  =  (27/b) * b^5     divide both sides by 27  and simplify

2187/ 27  =  b^4

81  =  b^4       take the positive 4th root

81^(1/4) =  b   =   3

And    27/b = a =    27/3   =  9

So....the function  is

y =  9 * 3^x