# The number of bacteria in 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 $2^{nd}$ hour, $4^{th}$ hour and $n^{th}$ hour?

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$=ar^{n}=30\times 2^{n}$
edited Mar 6, 2014