How many generations does it take for a single bacterial cell to become 256?

Question: How many generations does it take for a single bacterial cell to become 256?

To determine how many generations it takes for a single bacterial cell to become 256 cells, we can use the concept of exponential growth. Each generation doubles the number of cells.

The formula for exponential growth is:

$$ N = N_0 \times 2^g $$

where:

- \( N \) is the final number of cells,

- \( N_0 \) is the initial number of cells (which is 1 in this case),

- \( g \) is the number of generations.

We need to find \( g \) when \( N = 256 \):

$$ 256 = 1 \times 2^g $$

$$ 256 = 2^g $$

To solve for \( g \), we take the logarithm base 2 of both sides:

$$ g = \log_2(256) $$

Since \( 256 = 2^8 \):

$$ g = 8 $$

So, it takes 8 generations for a single bacterial cell to become 256 cells.