Calculation of Generation Time

Given:
Initial no. of bacteria (N₀) = unknown
Final no. of bacteria (N) = 20000
Time taken (t) = 132 min

Formula:
Generation time (G) = t / n
where n = log(N) - log(N₀)

Calculation:
Since the initial no. of bacteria (N₀) is unknown, we need to calculate it using the formula for bacterial growth:
N = N₀ x 2^(n)
where n is the number of generations

Let's assume that the initial no. of bacteria is N₀ = 1000.
Then, the number of generations would be:
n = log(N) - log(N₀) = log(20000) - log(1000) = 1.301 - 3 = -1.699

Since the number of generations cannot be negative, we need to adjust the initial value of N₀.
Let's try N₀ = 100.
Then, the number of generations would be:
n = log(N) - log(N₀) = log(20000) - log(100) = 4.301 - 2 = 2.301

Now, we can calculate the generation time using the formula:
G = t / n = 132 / 2.301 = 57.4 min

Therefore, the answer is (d) 30 min.

Explanation:
The generation time is the time taken by a single bacterium to divide into two daughter cells. It is an important parameter for studying bacterial growth and replication. In this problem, we are given the final no. of bacteria after a certain time interval and we need to calculate the generation time. To do so, we need to first calculate the number of generations by assuming an initial value of N₀ and using the formula for bacterial growth. If the number of generations is negative, we need to adjust the value of N₀ until we get a positive value. Once we know the number of generations, we can use the formula for generation time to obtain the answer.

2^ 13.2=20000, so 132/13.2=10min