An exponential function f ( x ) = a b x passes through the points (0, 4) and (3, 256). What are the values of a and b ?

Answer 1

f(x) = A*b^x

4 = A*b^0 = A*1 = A

so A=4

the function is f(x) 4 * b^x

256 = 4*b^3

64 = b^3

cube root of both sides says:

b = 4

f(x) = 4*4^x = 4^(x+1)