The number of bacteria in a certain culture doubles every hour. If there were 30 bacteria present in the culture originally, how many bacteria will be present at the end of the $2^{\text{nd}}$ hour, $4^{\text{th}}$ hour and $n^{\text{th}}$ hour?

Let $B_0 = 30$ be the initial count.

After each hour the count doubles, so $B_n = 30 \times 2^n$ (after $n$ hours).

End of $2^{\text{nd}}$ hour: $30 \times 2^{2} = 30 \times 4 = 120$

End of $4^{\text{th}}$ hour: $30 \times 2^{4} = 30 \times 16 = 480$

End of $n^{\text{th}}$ hour: $B_{n} = 30 \times 2^{n}$