Question

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 $2^{nd}$ hour $4^{th}$ hour and $n^{th}$ hour?

Answer 1

It is given that the number of bacteria doubles every hour.
Therefore, the number of bacteria after every hour will form a G.P.
with first term $(a=30)$ and common ratio $(r=2)$
$\therefore a_3={ar}^2=\left(30\right){\left(2\right)}^2=120$
Therefore, the number of bacteria at the end of 2nd hour will be 480.
$a_5={ar}^4=\left(30\right){\left(2\right)}^4=480$
and $a_{n+1}={ar}^n=\left(30\right){\left(2\right)}^n$
Thus the number of bacteria at the end of nth hour will be $\left(30\right){\left(2\right)}^n$