Answer:
f(x) = 2(4^x)
Explanation:
Look at x = 0 in the table. It corresponds to f(x) = 2.
Now look at your answer:
f(x) = 4^x
Use x = 0:
f(0) = 4^0 = 1, but the table has f(0) = 2, so your answer is not correct.
Notice the numbers in the f(x) column. They are 2, 8, 32, 128.
Notice that they are 2 times perfect squares.
2 = 2 * 1
8 = 2 * 4
32 = 2 * 16
128 = 2 * 64
Try
f(x) = 2(4^x)
Now you have
f(0) = 2(4^0) = 2 * 1 = 2
f(1) = 2(4^1) = 2 * 4 = 8
f(2) = 2(4^2) = 2 * 16 = 32
f(3) = 2(4^3) = 2 * 64 = 128
and all the given points work.
Answer: f(x) = 2(4^x)