Question

A bacterium divides every $35$ minutes. If a culture containing ${10}^5$ cells/mL is grown for $175$ minutes, what will be the cell concentration per ml after $175$ minutes?

Answer 1

Since the bacterium doubles its number every 35 minutes, in a span of 175 minutes, it will divide successively for 5 times in geometric progression. So, if there was a single bacterium it would become 32 bacteria after 175 minutes. But in the above problem, the initial number of bacteria was ${10}^5$ cells/mL, therefore, it will become 32 x ${10}^5$ cells/mL at the end of 175 minutes.
1 --> 2 --> 4 --> 8 --> 16 --> 32.