Question

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?

Answer 1

four bacteria are in First generation

Answer 2

1 million

Let us assume that there are 'x' bacteria in the first generation. Number of Bacteria in generation 1 is : 8 Survive To produce Next 4 + Half of Previous

So, the number of bacteria till 7th generation is as follows;

1. In 2nd generation the no.of bacteria = $\frac{8x}{2}$ = 4x.  Given by, 32 Survive To produce Next 16 + Half of Previous
2. In 3rd generation = 16x. Given by, 128 Survive To produce Next 64 + Half of Previous
3. In 4th generation = 64x. Given by, 512 Survive To produce Next 256 + Half of Previous
4. In 5th generation = 256x. Given by, 2048 Survive To produce Next 1024 + Half of Previous
5. In 6th generation = 1024x. Given by, 8192 Survive To produce Next 4096 + Half of Previous
6. In 7th generation = 4096x. Given by, 32768 Survive To produce Next 16384 + Half of Previous

Hence 'x' = 1 million.

∴ The number in the first generation is 1 million.

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