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A bacteria gives birth to two new bacteria in each second and the life span of each bacteria is 5 seconds. The process of the reproduction is continuous until the death of the bacteria. initially there is one newly born bacteria at time t = 0, the find the total number of live bacteria just after 10 seconds :

A. $\Large\frac{3^{10}}{2}$ B. $3^{10}-2^{10}$ C. $243 \times\left(3^{5}-1\right)$ D. $3^{10}-2^{5}$ Answer: Option C
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Solution(By Apex Team)

Total number of bacteria after 10 seconds, $\begin{array}{l}=3^{10}-3^5\\ =3^5\times\left(3^5-1\right)\\ =243\times\left(3^5-1\right)\end{array}$ Since, just after 10 seconds all the bacterias (i.e. $3^{5}$) are dead after living 5 seconds each.

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