Question

A bacterial cell divides once every minute. It takes one hour to fill a cup. How much time will it take to fill half cup.

• A. 59 minutes
• B. 30 minutes
• C. 29 minutes
• D. 20 minutes

Answer 1

The correct option is A 59 minutes

Doubling time is one minutes for bacteria i.e. after every one minute number of bacteria become double. It is given that in 60 minutes full cup will be filled with bacteria, i.e. before one minute half cup filled with bacteria so it will take 59 minutes to fill half cup.
1 min = $2^1$ bacteria
2 min = $2^2$ bacteria
1 hr/60 min = $2^{60}$ bacteria = 1 cup.
$2^{59}\times 2=1cup$
$2^{59}=\frac{1}{2}cup$
i.e. 59 minutes.