Question

if a generation time for the bacterial cell is 20 minute and we obtain 64 bacterial cell in how much time if we start with two bacterial cell
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Answer 1

Answer:

in start time_

We have two cells

2 ×2= 4 cells ( after 20 minute)

after 40 minutes

4×2 = 8 cells

after 60 minutes

8×2 = 16 cells

after 80 minutes

16×2 = 32 cells

after 100 minutes

32×2 =64 cells

Answer 2

Given: Generation time of bacteria = 20mins

No. of cells required at the end = 64

To Find: Time taken to obtain 64 cells

Solution:

Bacterial growth follows an exponential manner. It can be calculated using the formula:

No. of bacteria = 2ⁿ, where n is the number of generations.

Number of generations (n) = $\frac{Time}{Generation Time}$

Generation time is the time period in which all the bacteria present in the previous generation are able to reproduce and a new generation is formed.

Here, no. of bacteria = 64

64 = 2ⁿ

Let us factorize 64 as a multiple of 2

2x2x2x2x2 = 2ⁿ

2⁵ = 2ⁿ

On comparing, we get n = 5

So, in the fifth generation, we will obtain 64 cells

5 =  $\frac{Time}{Generation Time}$

5 = $\frac{Time}{20}$

Time = 5x 20

        = 100 mins

        = 1 hr 40 mins             (as 1 hr = 60 mins)

Therefore, we will obtain 64 bacterial cells in 1 hr 40 mins.