1. **State the problem:** We are given a sequence with terms $a_1=2$, $a_2=4$, $a_3=8$, $a_4=16$, $a_5=32$, $a_6=64$. We want to find which function rule represents this sequence. 2. **Identify the type of sequence:** The sequence doubles each time, so it is a geometric sequence where each term is multiplied by a common ratio $r$ to get the next term. 3. **General formula for geometric sequences:** $$a_n = a_1 \times r^{n-1}$$ where $a_1$ is the first term and $r$ is the common ratio. 4. **Find the common ratio $r$:** $$r = \frac{a_2}{a_1} = \frac{4}{2} = 2$$ 5. **Write the function rule:** $$a_n = 2 \times 2^{n-1}$$ 6. **Check the options:** - $f(n) = 2(4)^{n-1}$: This would give $a_2 = 2 \times 4^{1} = 8$, which does not match $4$. - $f(n) = 2(2)^{n-1}$: This matches our formula and sequence. - $f(n) = 2(3)^{n-1}$: This would give $a_2 = 2 \times 3^{1} = 6$, which does not match $4$. - $f(n) = 2(5)^{n-1}$: This would give $a_2 = 2 \times 5^{1} = 10$, which does not match $4$. **Final answer:** The function rule that represents the sequence is $$f(n) = 2 \times 2^{n-1}$$ This function correctly generates the terms of the sequence by starting at 2 and multiplying by 2 each time.