Question

A bacterium has a generation time of \(30\) minutes. Starting with \(1\times10^4\) (\(10000\)) cells, how many cells will be present after \(2\) hours?

• A. \(4\times10^4\)
• B. \(8\times10^4\)
• C. \(1.6\times10^5\)
• D. \(6.4\times10^5\)

Hint:

Bacterial population growth follows \[ \boxed{ N=N_0\,2^n, } \] where \[ n=\frac{\text{Total Time}}{\text{Generation Time}}. \]

Answer 1

The Correct Option is C

Step 1: Determine the number of generations. Given, \[ \text{Generation time}=30\text{ min}. \] Total time, \[ 2\text{ hours}=120\text{ min}. \] Hence, \[ n=\frac{120}{30}=4. \]

Step 2: Use the bacterial growth formula. The number of cells after \(n\) generations is \[ \boxed{ N=N_0\,2^n, } \] where
• \(N_0=10^4\),
• \(n=4\). Therefore, \[ N = 10^4\times2^4 = 10^4\times16 = 1.6\times10^5. \] Hence, \[ \boxed{1.6\times10^5} \] is the correct answer. Therefore, \[ \boxed{(C)} \] is the correct answer.