Write an exponential function in the form y=ab ^x that goes through points (0,4) and (2,256).

Answer 1

y = ab^x plug in (0,4) to solve for a

4 = ab^0 = a (any number to the zero power = 1)

a = 4(1) = 4

a = 4

y = 4b^x

plug in the other point (2, 256) to solve for b

256 = 4(b)^2

b^2 - 256/4 = 64

b = square root of 64

b = 8

y = 4(8)^x is the exponential function through the two given points.