What are the values of an and b ?

Question

An exponential function f(x)=ab^x passes through the points (0,12) and (3,96). What are the values of an and b?

Answer 1

f(x) = ab^x

substitute (0,12) for x and f(x)

12 = ab^0

since anything to the zero power is 1

12 = a

substitute (3,96) for x and f(x)

96 = ab^3

substitute 12 for a

96 = 12 b^3

8 = b^3

2 = b