Question

If a bacterial cell divides once every minute and take 23 minutes to fill a bottle. How much time it will take to fill half the bottle.

• A. 24 min
• B. 22 min
• C. 46 min
• D. 21 min

Answer 1

The correct option is B 22 min

No. of cells intially = 1

After 1 min, the number of cells will be $2\times 1=2^1$

After 2 min $=2\times 2=2^2$

After 3 min $=2\times 2\times 2=2^3$

So, after 23 min, the number of cells will be $2^{23}$

Quantity of the bottle $=2^{23}$

Quantity of half of the bottle $=\frac{2^{23}}{2}=2^{22}$

After 22 minutes, the number of cells $=2^{22}$

Thus, time taken to fill half of the bottle =22 min