y = 8(2)^ x
the general form of an exponential function is y = a × b^ x
to find a and b substitute the given points into the general equation
(1 , 16) → 16 = ab → (1)
(4 , 128) → 128 = ab^ 4→ (2)
divide equation (2) by equation (1)
ab^ 4 / ab = 128/16 ⇔ b³ = 8 ⇒ b = 2
substitute b = 2 into equation (1)
2a= 16 ⇒ a = 8
equation is y = 8 (2)^ x