To find the function that best represents the data in the table, let’s observe the pattern in the values of \( f(x) \):
- When \( x = 0 \), \( f(0) = 2 \)
- When \( x = 1 \), \( f(1) = 8 \)
- When \( x = 2 \), \( f(2) = 32 \)
- When \( x = 3 \), \( f(3) = 128 \)
- When \( x = 4 \), \( f(4) = 512 \)
Now let’s look for a function that fits this pattern:
First, notice how the function values seem to scale up quickly:
- \( 2 \) can be written as \( 2 \times 4^0 \)
- \( 8 \) is \( 2 \times 4^1 \)
- \( 32 \) is \( 2 \times 4^2 \)
- \( 128 \) is \( 2 \times 4^3 \)
- \( 512 \) is \( 2 \times 4^4 \)
This leads us to conjecture that the function could be written as \( f(x) = 2 \times 4^x \).
Now looking at the given options, the only one that matches our finding is:
f(x) = 2(4^x)
Thus, the correct response is:
f of x is equal to 2 times open paren 4 to the x th power close paren.