To calculate the number of bacteria after 4 generations when starting with \(10^4\) bacteria, it's important to first understand how bacteria reproduce.
If we assume that the bacteria double every generation, the formula for the number of bacteria after \(n\) generations, starting from an initial population \(P\), is given by:
\[ P_n = P \times 2^n \]
Where:
- \(P_n\) is the number of bacteria after \(n\) generations,
- \(P\) is the initial number of bacteria,
- \(n\) is the number of generations.
In your case:
- \(P = 10^4 = 10000\),
- \(n = 4\).
Now, substituting these values into the formula gives:
\[ P_4 = 10000 \times 2^4 \]
Calculating \(2^4\):
\[ 2^4 = 16 \]
Now substituting that value back in:
\[ P_4 = 10000 \times 16 = 160000 \]
Therefore, the number of bacteria present after 4 generations will be 160,000.
1 answer