Exponential Growth Analysis: Identifying Properties in the Set 2, 4, 8, 16, 32, 64

To solve this problem, let's analyze the sequence of numbers given: $2, 4, 8, 16, 32, 64$.

First, let's calculate the ratio between each pair of consecutive terms in the sequence:

• The ratio of the second term $4$ to the first term $2$ is $\frac{4}{2} = 2$.
• The ratio of the third term $8$ to the second term $4$ is $\frac{8}{4} = 2$.
• The ratio of the fourth term $16$ to the third term $8$ is $\frac{16}{8} = 2$.
• The ratio of the fifth term $32$ to the fourth term $16$ is $\frac{32}{16} = 2$.
• The ratio of the sixth term $64$ to the fifth term $32$ is $\frac{64}{32} = 2$.

Each consecutive term is obtained by multiplying the previous term by $2$. Therefore, this sequence is a geometric sequence where each term is $\times 2$ times the preceding term.

This consistent multiplication factor shows that the sequence's property is that of a geometric progression with a common ratio $r = 2$.

In conclusion, the identified property of the sequence is that each term is multiplied by $2$, which is option $\times 2$.