A bacterium divides every 35 minutes.  If a culture containing $1\times 10^{5}cells/mL$ is grown for 175 minutes, what will be the cell concentration / mL after 175 minutes ?

The time required for a bacterial population to double is known as the generation time. In this case, the bacterium divides every 35 minutes, so its generation time (t) is 35 minutes.

To calculate the final cell concentration after 175 minutes of growth, we need to determine how many generations will occur during that time:

Number of generations = (total time) / (generation time)
Number of generations = 175 minutes / 35 minutes
Number of generations = 5

So, the initial cell concentration is 1 × 10^5 cells/mL, and the number of generations that occur during 175 minutes of growth is 5. Therefore, the final cell concentration can be calculated using the following formula:

Final cell concentration = (initial cell concentration) × 2^(number of generations)

Final cell concentration = (1 × 10^5 cells/mL) × 2^(5)
Final cell concentration = 1 × 10^5 cells/mL × 32
Final cell concentration = 3.2 × 10^6 cells/mL

Therefore, the cell concentration after 175 minutes of growth will be 32 × 10^5 cells/mL.