The equation of a exponential function that passes through (1,16) and (4,128)

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

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