how do you solve an exponential function?

Question

An exponential function that passes thru the points (1,4) and (3, 64)

Answer 1

f(x) = AB^x ; B > 0

 

f(1) = AB = 4

 

f(3) = AB³ = 64

 

f(3)/f(1) = AB³/(AB) = B² = 64/4 = 16

 

B = √16 = 4

 

A = 4/B = 4/4 = 1

 

f(x) = 4^x