One bacterium splits into eight bacteria of the next generation. But due to environmental condition only 50% survives and remaining 50% dies after producing next generation. If the seventh generation number is 4,096 million, what is the number in first generation?
- 1 million
- 2 million
- 4 million
- 8 million
let's say x is the initial number of bacterias :
So in 2nd generation no. of bacterias = 8x, but due to environment condition 50% dies
Therefore 8x/2 = 4x
We can say that every new generation is 4 times the previous generation.
In 3rd generation, it will be = 16x
4th gen. = 64x
5th gen. = 256x
6th gen. = 1024x
7th gen. = 4096x
Hence x = 1 million