Given:
- Cell division time = 1 minute
- In 20 minutes, the culture tube is 1/8th filled with cells

To find:
- Time required for the tube to be fully filled with cells

Solution:

Let's assume that at t=0 minutes, the culture tube is empty.

After 1 minute (t=1), one cell will divide into two. So, we will have 1 cell in the tube.

After 2 minutes (t=2), the 1 cell will divide into 2 cells. So, we will have 2 cells in the tube.

After 3 minutes (t=3), the 2 cells will divide into 4 cells. So, we will have 4 cells in the tube.

Similarly, after 4 minutes (t=4), we will have 8 cells in the tube.

After 5 minutes (t=5), we will have 16 cells in the tube.

After 6 minutes (t=6), we will have 32 cells in the tube.

After 7 minutes (t=7), we will have 64 cells in the tube.

After 8 minutes (t=8), we will have 128 cells in the tube.

We can see that the number of cells in the tube is doubling every minute.

Now, we are given that in 20 minutes, the tube is 1/8th filled with cells.

At t=8 minutes, we have 128 cells in the tube.

At t=9 minutes, we will have 256 cells in the tube.

At t=10 minutes, we will have 512 cells in the tube.

At t=11 minutes, we will have 1024 cells in the tube.

At t=12 minutes, we will have 2048 cells in the tube.

At t=13 minutes, we will have 4096 cells in the tube.

At t=14 minutes, we will have 8192 cells in the tube.

At t=15 minutes, we will have 16,384 cells in the tube.

At t=16 minutes, we will have 32,768 cells in the tube.

At t=17 minutes, we will have 65,536 cells in the tube.

At t=18 minutes, we will have 131,072 cells in the tube.

At t=19 minutes, we will have 262,144 cells in the tube.

At t=20 minutes, we will have 524,288 cells in the tube.

We are given that at t=20 minutes, the tube is 1/8th filled with cells.

So, at t=20 minutes, the tube has 1/8th of its capacity filled with 524,288 cells.

Let's assume that the tube can hold a maximum of X cells.

So, (1/8)X = 524,288

X = 4,194,304

This means that the tube can hold a maximum of 4,194,304 cells.

Now, we need to find the time required for the tube to be fully filled with cells.

The tube is fully filled when it has 4,194,304 cells.

We have already seen that the number of cells in the tube is