If a bacterial cell divides once every minute and takes 60 minutes to fill a cup. How much time it will take to fill half cup? (1)30 min (2)32 min (3) 29 min (4) 59 min ?

Question

Answer

59 min
The growth of bacteria is exponential .So 1 bacterium doubles and Form two bacteria these 2 doubles and form 4 . Similarly, half cup of bacteria double and become a full cup in the 60th minute

Answer

In 1 min,a single bacteria turns into two=2^1=2
In 2 min,these two bacteria again turn into two=2^2=4
In one hour=2^60,it takes 60 min to fill the cup.
Half the quantity implies (2^60)/2=(2^59).
Hence,it takes 59 min to fill half of the cup.
Ans:59 minutes

Answer

**Answer:**

To determine how long it will take to fill half a cup, we need to understand the relationship between the time it takes for a bacterial cell to divide and the time it takes to fill a cup.

**Time for a Bacterial Cell to Divide:**
Given that a bacterial cell divides once every minute, we can assume that each division results in two bacterial cells. This means that after 1 minute, there will be 2 cells. After 2 minutes, there will be 4 cells, and so on.

**Time to Fill a Cup:**
If it takes 60 minutes to fill a cup, we can assume that the cup starts with 1 bacterial cell, and after 60 minutes, it is completely filled.

Now, let's calculate how long it will take to fill half a cup.

**Calculating the Time to Fill Half a Cup:**
To fill half a cup, we need to determine how many cells are needed.

- The cup is completely filled with bacteria after 60 minutes.
- After 1 minute, there are 2 cells.
- After 2 minutes, there are 4 cells.
- After 3 minutes, there are 8 cells.
- After 4 minutes, there are 16 cells.
- And so on.

We can see that the number of cells doubles every minute. Therefore, after n minutes, the number of cells is given by 2^n.

To fill half a cup, we need to have half the number of cells as we have at the end of 60 minutes.
Let's calculate the number of cells required to fill half a cup:

- Half the number of cells at 60 minutes = 2^(60-1) = 2^59

Therefore, it will take 59 minutes to fill half a cup.

**Final Answer:**
The correct answer is (4) 59 minutes.

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