Answer:
Option B is correct
![f(x) = 4^x](https://tex.z-dn.net/?f=f%28x%29%20%3D%204%5Ex)
Step-by-step explanation:
Exponential function is of the form:
![f(x) = ab^x](https://tex.z-dn.net/?f=f%28x%29%20%3D%20ab%5Ex)
where a is the initial amount and b is the growth factor.
Consider any two points from the given tables:
(3, 64) and (4, 256)
Substitute in [1] we have
.....[2]
.....[3]
Divide equation [3] by [2] we get;
![4 = b](https://tex.z-dn.net/?f=4%20%3D%20b)
Substitute the value of b in [2] we get;
![64 = a(4)^3](https://tex.z-dn.net/?f=64%20%3D%20a%284%29%5E3)
![64 = a \cdot 64](https://tex.z-dn.net/?f=64%20%3D%20a%20%5Ccdot%2064)
Divide both sides by 64 we get;
1 = a
or
a = 1
⇒![f(x) = 4^x](https://tex.z-dn.net/?f=f%28x%29%20%3D%204%5Ex)
therefore, the exponential function represents the data in the table is, ![f(x) = 4^x](https://tex.z-dn.net/?f=f%28x%29%20%3D%204%5Ex)