Question

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

Answer 1

Bacteria prresent in the culture originally = 30

Since the bacteria doubles itself after each hour. So the sequences of bacteria after each hour is a G.P

Here a = 30 and r = 2

So bacteria at the end of $2^{nd}$ hour

= $30\times 2^{3-1}=30\times 2^2=120$

bacteria at the end of $4^{th}$ hour

= $30\times 2^{5-1}=30\times 2^4=480$

Bacteria at the end of $n^{th}$ hour

= $30\times 2^{n+1-1}=30\times 2^n$