Hi,
Initially, it will be 8x. Since 50% of it die, there will be only 4x left.

Hi,

x = first-generation bacteria

This will split into 8x out of which 50 % will die => only 4x will be alive in 2nd generation

4x will become 32x in 3rd generation out of which only 16x will survive(3rd generation)

16x will become 128x in 4th generation out of which only 64x will survive ( 4th generation)

and so on

Hope this helps.

Hi,

After splitting, half of them die. Initially if there 1bacteria, it will split into 8 out of which 4 will die and remaining 4 survives.

No, the new bacteria die even before they can reproduce. 
So 1 --> 4 who can reproduce + 4 who die immediately.

Remaining 50 % dies after producing next generation. Doesn't it means that they will produce next generation ?

Hi Krutik,
We have updated the question and made the necessary changes. Please have a look and let us know in case of any issue.
Hope this helps

Hi Kishore,
let's say x is the initial number of bacterium :
As half will die and half become 8 times.
So in 2nd generation no. of bacterium = $$8\times\ \ \frac{\ x}{2}$$​= 4x
In 3rd generation, it will be = $$8\times\ \ \frac{\ 4x}{2}$$ =16x
Similarly in 4th gen. = 64x
5th gen. = 256x
6th gen. = 1024x
7th gen. = 4096x
In 7th generation we have 4096x.
It is given in question that 4096 million bacterium present in 7th generation.
So 4096 = 4096x
Hence x = 1 million
Hope this helps!