Given that there were $30$ bacteria present originally.

$\therefore a=30$

Also given that the number doubles every one hour.

$\therefore\;$ After one hour the count =$2\times 30=60$

Since the count doubles every hour it forms a G.P. with $r=2$

$a, ar, ar^2........$

$\Rightarrow\:$ The count at the end of $2^{nd}$ hour$=a.r^2=30\times 2^2=120$

$\Rightarrow\:$ The count at the end of $4^{th}$ hour$=ar^4=30\times 2^4=480$

$\Rightarrow\:$ The count at the end of $n^{th}$ hour$=ar^{n}=30\times 2^{n}$