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.
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