In the first year Geoff's garden produced 4 bulbs, in the second year it produced 8, and the third 16. How many bulbs will geoff's garden produce on the 10th year?

Question

A: 2,048
B: 1,024
C: 40
D: 32

Answer 1

We notice that the number of bulbs produced each year is a power of 2, specifically $2^0=1$ in the first year, $2^1=2$ in the second year, and $2^2=4$ in the third year.

If we continue this pattern, we see that the number of bulbs produced in the $n$th year is $2^{n-3}$. Therefore, the number of bulbs produced in the 10th year is $2^{10-3}=2^7=\boxed{\textbf{(D) }32}$.