Question

number of mitotic division involved for production of 64 cells

Answer 1

Since one mitotic division leads to formation of 2 cells , we can mathematically express this as

No of cells = 2^n (n= no. of mitotic divisions)

→64= 2 ^n

→2^6= 2^n

→n=6

therefore 6 mitotic divisions lead to formation of 64 cells .

Hope it helps :)

Answer 2

I am not really sure if you are refering to number of generations/cycles that it took to reach from 1 to 64 or number of cells that underwent mitotic divisions. I will give you both answers, nonetheless.

So let's start with one cell

To have 2 daughters there will be one mitotic division.

In next generation you will have 2nd cycle in 2 cells undergoing mitosis giving you 4 cells. So till now you have 1+2 mitotic divisions.

For 3rd cycle you will get 8 cells from 4 mitotic divisions

In 4th you will have 16 daughter cells from 8 mitotic divisions

For 5th 32 cells from 16 divisions.

For 6th you have 64 cells from 32 divisions.

So total number of generation /cycles required are ln(64) = 32. Number of cells that underwent mitotic divisions are 32+16+8+4+2+1 = 63. So for N number of daughter cells N-1 cells undergo mitotic divisions in n = ln(N) generations