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?

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.