2. Bacteria reproduce asexually by dividing into two every ten minutes. How many bacteria were there at the beginning if there were $2^{17}$ after two hours?
2. Bacteria reproduce asexually by dividing into two every ten minutes. How many bacteria were there at the beginning if there were $2^{17}$ after two hours?

## Solution.

Two hours have 120 minutes, so the number of bacteria doubles 12 times. After two hours, we have $2^{12}$ times more bacteria than at the beginning.

Since there were $2^{17}$ after two hours, the number of bacteria at the beginning was

$$
\begin{aligned}
& 2^{17}: 2^{12} \\
& =2^{5}=32
\end{aligned}
$$

Note: The solution and numbers that appear in the intermediate steps can, but do not have to, be written in the form of powers with base 2.