In 20 min culture medium filled 1/8th
in 21 min filled its double i.e 2/8= 1/4th.( in 1min each divide to form 2 cells). similarly in 22 min it filled 2/4=1/2.
& in 23rd min it get filled completely i.e 2/2=1....

The Problem:
We are given that the generation time of a cell is 1 minute. After 20 minutes, a culture medium is 1/8th filled with cells. We need to determine when the medium will be completely filled.

Understanding the Problem:
To solve this problem, we need to understand the concept of generation time. Generation time is the time it takes for a cell to divide into two daughter cells. In this case, the generation time is given as 1 minute.

Approach:
To solve the problem, we can use the concept of exponential growth. In exponential growth, the number of cells doubles in each generation. Let's break down the problem into smaller steps:

1. Calculate the number of generations that have occurred in 20 minutes.
2. Determine the current population of cells in the culture medium.
3. Calculate the number of generations required for the culture medium to be completely filled.
4. Calculate the time required for the medium to be completely filled.

Step 1: Calculate the Number of Generations in 20 Minutes:
Since the generation time is 1 minute, the number of generations that have occurred in 20 minutes is simply 20 divided by 1, which equals 20 generations.

Step 2: Determine the Current Population of Cells:
We are given that after 20 minutes, the culture medium is 1/8th filled with cells. This means that the current population of cells is 1/8th of what it would be when the medium is completely filled. Let's represent the current population as "X".

If the medium is completely filled after "N" generations, then the current population "X" is given by the equation:
X = (1/2)^N

Since the current population is 1/8th of the final population, we have:
1/8 = (1/2)^N

To solve for "N", we can rewrite the equation as a logarithm:
log(1/8) = log((1/2)^N)
log(1/8) = N * log(1/2)

Using logarithmic properties, we can simplify the equation:
log(1/8) = N * (-log(2))
log(8) = N * log(2)
3 = N * 0.3010
N ≈ 9.97

Therefore, the current population of cells is X ≈ (1/2)^9.97.

Step 3: Calculate the Number of Generations for Complete Filling:
To determine the number of generations required for the culture medium to be completely filled, we need to find the smallest integer value greater than or equal to N. In this case, the smallest integer greater than or equal to 9.97 is 10.

Therefore, the number of generations required for complete filling is 10.

Step 4: Calculate the Time Required:
Since each generation takes 1 minute, the time required for complete filling is simply 10 minutes.

Final Answer:
The medium will be completely filled after 23 minutes.