Question

One bacteria splits into eight bacteria of the next generation. but due to environment, only 50% of a generation survive. if the eighth generation number is 8192 million, what is the number in the first generation?

Answer 1

the answer is 1 million.
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Answer 2

Answer:

The number in the first generation is 500,000

Explanation:

The first number of bacteria after split is $=8\left(n^{2} \frac{x}{2}\right)$, that is the eighth part of the half bacteria divided.

According to this the number of divisions are 8, therefore the value of bacterium division are:

$n \epsilon 0,2,4,8,16, \ldots \ldots \ldots \ldots, 8\left(n^{2} \frac{x}{2}\right)=8\left(\frac{x}{2}\right), 8\left(4 \frac{x}{2}\right), 8\left(16 \frac{x}{2}\right)$

Making the common ratio of the geometric progression as 4

Now, the seventh generation bacteria number is given as 4096

$G . P .=a_{n}=a r^{n-1}$

$8192 \text { million }=x(4)^{7}$

$\frac{8192 \text { million}}{(4)^{7}}=x$

$0.5 \text { million }=x$

Therefore, the value of the first generation bacteria is 500,000.