The number of bacteria in a certain culture doubles every

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The number of bacteria in a certain culture doubles every hour. If there were 50 bacteria present in the culture originally, how many bacteria will be born in 12th hour ?

1. 102460
2. 120450
3. 102400
4. 120400

Correct Option: C

The number of bacteria at any given time forms a GP whose terms are given by 50, 100, 200, ... where
a = 50, r = 100/50 = 2
T_n = ar^{n -1}
⇒ T₁₂ = 50(2)^{12 - 1}
= 50 x (2)¹¹
= 102400
So, the number of bacteria born in 12th hour is 102400.